show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Evaluate the second derivative at this critical number.

A:

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

A:

Q: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

A:

Q: Find the Derivative of f(x)= tan(- -3

A: We have to find the derivative of function: fx=tan x3x2-3 We know the formula of derivatives, d tan…

Q: Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16…

A: The tangent line is horizontal where y'=0

Q: By using the second derivative test for functions of two variables, find three positive numbers…

A:

Q: Compute the derivative using derivative rules that have been introduced so far y = √(9 +x + sinx)

A: We have to compute derivative of the function: y=9+x+sin x We know the formula of derivatives,…

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Find the derivative of the function without using the Quotient Rule. y

A:

Q: Explain how to apply the Second Derivative Test.

A: The second derivative test is used to find the relative maxima or relative minima. The second…

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: What is the 28th derivative of sinx?

A: Option D is correct

Q: Derive the derivative function for secx and express your answer in product form.

A: ddx(secx)=ddx(1cosx)ddx(secx)=cos(x)ddx(1)-1ddx(cos(x))cos(x)2ddx(secx)=cos(x)0-1-sinxcos(x)2ddx(sec…

Q: find the derivative oof 1/x^3 + 3* 1/square root of x

A:

Q: Find anti-derivative if possible of: sqrt(tan(x))  dx

A:

Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: Compute the derivative using derivative rules that have been introduced so far y = cos4 θ

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: can you solve the derivative function or what is the corect derivative of this function?

A: We have to find derivative of given  function.

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Evaluate the 2nd derivative at the given point.

A: We differentiate both sides with respect to x. Then we plug the given point.

Q: Find the derivative fex=exV3x+2

A:

Q: Find the derivative of the function without using the Quotient Rule. y =

A:

Q: Estimate the derivative of f(x) = sinx atx = ~-

A: Consider the provided function, fx=sinx at x=π2 Find the derivative of the function. First, we…

Q: Compute the derivative using derivative rules that have been introduced so far y = ex-12

A: To differentiate y=ex-12, with respect to x, apply the exponential rule of differentiation,…

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: derivative of f(x)= 3sin2x

A:

Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: What is sign analysis of first derivative?. When a function is said to be increasing, decreasing…

A: As per our guidelines, I have solved the fourth problem. If you want the answer of the fifth…

Q: Compute the derivative using derivative rules that have been introduced so far       y = √(7x - 3)

A: To find the derivative: y=(7x-3) Solution: y=(7x-3) Differentiating both sides w.r.t x we get:…

Q: Find the anti-derivative of

A: Answer and explanation is given below

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: Find the derivative of the function. f(x) = /5 +x sec x [5+x secx

A:

Q: What is the Derivative of: y = extan x

A: Given: y=ex tan x To Find: dydx=?

Q: State the First Derivative Test.

A:

Q: In(X+ bnx) %3D

A:

Q: What is the derivative of y=(1-x-1)-1  Please show steps. Thanks.

A:

Q: In(x-

A:

Q: Find the  1st derivative of : y-=sec3β tan2β

A:

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: Find the derivative of f(x)=5-x/2sin2x

A: Consider the given function.

Q: (x² +2)S UI -人 S-X

A: →First of all, simplify the given expression using logarithmic property.              ln(ab) = ln(a)…

Q: Find the derivative of using first principle?

A: we have to find first derivative of y by using first princple