Find the first derivative or f(x) of the following functions using the techniques of integration.

Q: 9)/6)= (2x+1)*

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the second derivative of the following function: f(x) = esinx %3D

A:

Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: Find the derivative of the function F(s) = In(9 ln(8s)). F'(s)

A:

Q: What is the first derivative of s(x) = 4e.

A: Given function - s(x) = 4ex-3Differentiating on both sides with respect to x - ddxs(x) =…

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: What is the millionth derivative of f(x) = e x ?

A: ex

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

A:

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

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Q: What is the second derivative of f (x) = e²?

A:

Q: Find the derivative of the function.

A: Given: f(x)=log2x2x-1

Q: Find the derivative of the following function with respect to x x = sinh2y

A:

Q: Find the derivative of the function

A:

Q: compute a formula for the nth derivative of f(x)=e2x

A: We have givenWe have to find a formula for nth derivative of f(x)

Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: 3 Find the first derivative of f (x) = 3x e

A: Given that : f(x)= x3 / e3x. Find the first derivative of this function. We know that d(xn)/dx =…

Q: Determine the 3rd derivative of the function y=x3/x+2 at x=−1.

A:

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by…

A: Consider the given function:

Q: Find the derivative of f(x) = In (x* V8 – 6x), using the properties of the logarithm. Provide your…

A: I have stated the used formulas in the solution

Q: Find the derivative of the function. f(x) = ln 2x/(x + 3)

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Q: Find the first derivative of the function * 4 f (x) = Væ + 4

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: Calculate the derivative of this following functions: i. log,,(x* – 7) ii. ecos2x

A: Given

Q: Find the first derivative of with respect to x using the increment method y=3x^2-7x+12

A:

Q: f(x) = e*

A:

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: f(x) = 400(15 – x²)(3x - 2)

A:

Q: Find the second-order derivative of the following function: f(x) = log2 cos x + ln π

A: We have to solve

Q: 1. y, x= 1+ 1+y

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Q: y = V5х+7

A:

Q: Find the derivative of the function. h(x) = log,(x² + x) h'(x) %3D

A: Given query is to find the derivative of the expression.

Q: 8x+9 In(, x3 dx

A: Here we will sove derivative of given function,

Q: Find the derivative of the function. f(x) = ln x/(x2 + 1)

A:

Q: 1 Find the derivative of the function : ƒ(x ) = V |2x + 3

A: The given function is: f(x)=12x+3 Let, u=2x+3. So, f(u)=1u=u-12 and u=2x+3

Q: Find the derivative of the function.

A:

Q: What is the second derivative of * f(x) = e²?

A: We have to find second derivative of the function: fx=ex2 We know the formula of derivatives,…

Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: Find the derivative of the function. F(x) etd dt F'(x) =

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Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

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Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

Q: Find the second derivative of f(t) = ln(sin² (t)).

A: Given data: The given function is f(t)=ln(sin2(t)). The expression for the first derivative of the…

Q: 8.) f(x) = v5x6 – 12 10.) f(x) = (x - 4x- 7)

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Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A:

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

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