Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

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Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Find the second derivative of the function. f(x) = cos(2x?) f "(x) =

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Q: F(x) = f Cos t dt

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: f(x) = cos (x – a -2).

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Q: 1 dx = +C (x+1)² X+1

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function, h(x):…

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Q: Compute the derivative of f(x) = (sin x)v , 0 < x < T.

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Q: Find the second derivative of the function f(x) = x sin(x) + cos(x)

A: The given function is fx=xsinx+cosx.  The product rule of the derivative is :…

Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. G(x) =…

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Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Find the second derivative of f(x) * f(x) = cos² 7x

A: The given function is: fx=cos27x   As we know that; The Chain Rule: fgx'=f'gx·g'x The Product Rule:…

Q: Find the derivative of f(x) = x² cos r.

A: The given function fx=x2cosx Differentiate with respect to x using the product rule…

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: Find the derivative of the function

A: Given function, Fx=∫πlnxcoset dt

Q: Find the second order derivatives of the function f(x) ex sinx cos 2x

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Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Find the 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Find y' in the function In (xy + x+ y) = 2 using implicit differentiation.

A: The given equation is: ln (xy+x+y)=2...(1)

Q: Find the derivative of the function y=cos(3 In x).

A: Given y=cos(3lnx)

Q: Use the technique of log differentiation to find when y = (sin(x))In(x) %3D dx and then evaluate it…

A: Given that y=sinxlnx find dydx using log differentiation

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: dx = +C (x+1)² X+1

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Q: Where is the function sin (log (r2 + y²)) continuous?

A: Function = Sinlogx2+ y2

Q: 2. Use logarithmic differentiation to find y' a) y = xcosx b) y = cosx* c) y = (Vx)2x

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Q: Use the Fundamental Theorem of Calculus to find the derivative of h(x)= (from -4 to sin of…

A: This is a calculus problem

Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

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Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: Find the derivative of F(x) = n sin(t) dt. 3x2 d dx cos(x)

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Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: f(t) = sin²(e in²s) %3D

A: Given : ft = sin2esin2t

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: Find the first derivative of f = (h+2)² (2h+1) h²+3 V using logarithmic differentiation

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Q: Verify the differentiation formula.

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

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Q: Use logarithmic differentiation to find the derivative of y with respect to x. y = ( In (3x))n (9×)…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: