Find f. f '(x) = 5/sqrt(1-x^2)                         f(1/2)=3

Q: Find the 7th derivative of: f(x)=sin(x)cos(x) f’=? • • •

A:

Q: fla)=-sinx (): In, Cosx

A:

Q: Find the derivative of the function. f (x) = cube root of ( 1+ tant )

A:

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

A:

Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

Q: Find the derivative of x/ex^2.

A:

Q: Find the most general anti-derivative or indefinite integral and check the answer by differentiation…

A:

Q: 29. Find the 5th derivative ofy= sin2x

A: 29. Given function is, y=sin2x. The first derivative of y is, y'=ddxsin2x=cos2x·2=2cos2x   The…

Q: ) y = In³ )) (tanh²(scc '(x²)

A:

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

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: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: tion of the tangent line to f(x) = 4 %3D

A:

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

A:

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

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

A:

Q: Find the derivative of the function f(x) = arctan ex

A: According to the question, we have to find the derivative of the function fx=arctan ex. The…

Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

Q: In(tanhx)

A: As we know that; The chain rule: fgx'=f'gx·g'x And ddxtanhx=sech2x Given: fx=lntanhx

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: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: sinx 3. f(x)=(x)*

A:

Q: Find the derivative f(x)= Inlex+9)

A: To find: the derivative of f(x)

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

A:

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: FInd the derivative of f(x) =ln 1+ex/1-ex

A:

Q: Find the second derivative if y = sinh- (n + x') at x = 0

A:

Q: Compute the derivative. Use logarithmic differentiation where appropriate. 10 1+ dx 10 1+ dx 10 In…

A: Answer: ddx1+10xx = ln1+10x-10x+10 1+10xx

Q: 1-sinx f(x) = V1+sin x

A: Since, you have asked multiple question , as per the company guidelines we will solve the first…

Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

A:

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: Find the 2nd derivative of the given function fCt) = t² Int

A:

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Compute the derivative ln(ex+1) / 2x+1

A:

Q: Find the derivative and simplify: f(x)=ex-cotx

A: To determine the derivative.

Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

A:

Q: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: What is the 2nd derivative of y=cosh(x+y)?

A:

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e'. =-e?. Equation:

A: As we know that the equation of the tangent line is: y-y1=mx-x1 Where 'm' is the slope. Given:…

Q: Find the derivative. Simplify where possible. y = x tanh  -1 x +ln ( sqrt 1 - x 2 )

A: Given, y=xartanh⁡(x)+ln⁡(1−x2)can be rewritten asy=ln⁡(1−x2)2+xartanh⁡(x)