Given the functions fz) = 3* and g(x) = sin x, determine the domain of the combined function y= fg(x)).

Q: What is the derivative of f(x) = 26 (12.1)* + 8 (0.56)* +1 ex with respect to x? f '(x) =

A: topic  -  derivative of exponential function

Q: Consider the function f(x) whose second derivative is f''(x) = 8x + 6 sin(x). If f(0) = 2 and f'(0)…

A: Given  f''(x) = 8x+6 sin(x),  f(0)=2,  f'(0)=4 We have to find the value of f(3).

Q: Differentiate f (x) = sin Vx by the first principle

A: Here we use the formula

Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: Assume that y = sin'x is a differentiable function of x. By differentiating the equation x= sin y…

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Q: Consider the function f(x) whose second derivative is f"(x) = 3x + 8 sin(x). If f(0) = 2 and f'(0)…

A: Consider the second derivative function, f''x=3x+8sinx Given, f0=2  and f'0=2 We need to find f(x).…

Q: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

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Q: 3x²+1 e) у %3D cos?(3x?) f) y = x-2

A: We need to evaluate the derivative of the following function e y = cos23x2f y = 3x2+1x-1

Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 9 sin(x). If f(0) = 4 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 2 sin(x). If f(0) = 3 and f'(0)…

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Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y = (x +…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: The derivative of the function y = tan-1 Vx2 – 1 + csc¬1 x, where x > 1 is: |

A:

Q: Consider the function f(x) whose second derivative is f''(x) 8x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given : f"(x) = 8x + 3 sinx, f(0) = 4, f'(0) = 4,    To find : f(5)?

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: Differentiate the following implicit function with respect to x: xy² -;=- cos (y?) a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: The derivative of f(x) = cos-(2x) is:

A:

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: The derivative of f(x) = 2 cos 2x is an odd function.

A: Odd function

Q: Consider the function f(x) whose second derivative is f"(x) = 6x + 5 sin(x). If f(0) = 4 and f'(0) =…

A: Using integration & given condition.

Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: r (4x2 – 3x + 5)* - 3.) c(x) = %3D sin x

A: solution:- find the derivative by using the quotient rule

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: Given r(z) = 3x + 4x +7x +4, find r'(x) using the definition of a derivative. answer.) Provide your…

A: Given -r(x)=3x4+4x2+7x+4...(1)as we have to calculate r'(x) therefore differentiate equation (1)…

Q: Given g(x) = In(11x³ + x), the derivative g (x) is %3D O 88z7 +1 11r8 +I 8z7 O 88z7 +1 O 11r8 + r O…

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Q: g(x)%3Dx sin(2*)

A:

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 6 sin(x). If f(0) = 2 and f'(0) =…

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Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: Given the function xye9-sin² ecos² fxx of f is equal to 0. f(x, y)= The second derivative Select…

A: A detailed solution is given below. fx = partial derivative of f(x,y) with respect to x. fxx =…

Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

A:

Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: Consider the function f(x) whose second derivative is f''(x) = 5x + 7 sin(x). If f(0) = 2 and f'(0)…

A: Given :f''(x)=5x+7sin(x)

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinaxdx=-cos(ax)a+c ∫cosax dx=sin(ax)a+c ; where 'c' is an integration…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f" (x) = 9x + 3 sin(x). If f(0) = 3 and f' (0)…

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Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: Find the derivative of the function f(x) = x sin(6x + 14)+ In(5z+9) Answer:

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Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: Q1) Compute the derivative of the function f (t)= | sin² x²dx. -t

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Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 2 and f'(0)…

A: We need to find f(5).