Consider the function h(x) = arcsin(5x). The function h can be written as the composition of a inner function, v(x), and an outer function, u(x). Identify the functions u(x) and v(x) and determine their derivatives. position function derivative Inner v(x) Outer u(x) What is u(v(x))? What is h(x)?

Q: Find the derivative of the function.

A: To find: The derivative of the function . Formula used: Chain rule of derivative: Derivative of the…

Q: Find the derivative. g(x) = cosh(In(x)) %3D g'(x) = | 0 %3D Need Help? Read It

A:

Q: 2. Find the derivative of y = 2 1 1- x² + arcsin x 2

A: As per our guidelines, I can answer only one question and maximum three subparts of a question.…

Q: Find the derivative of g(x) = In(sin²(ed/x)).

A:

Q: Using the Chain Rule, compute the first derivative of sin T-x.

A: We have given a composite function and we have to find derivative of function by using chain rule of…

Q: Find the derivative of cos(xy^2) = -3y using implicit differentiation

A:

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

A:

Q: Find derivatives of the function defined as follows.

A:

Q: Use implicit differentiation to calculate higher derivatives. Use the method of the previous…

A:

Q: Find the derivative of the function y = tan(arcsin x)

A:

Q: 1-x Find the derivative of y = arctan %3D 1+x

A:

Q: 10. g(x) = e*´ arcsin x

A: g(x)=ex2sin-1x We need to find the derivative of the given function.

Q: g) Use implicit differentiation to find y, given x' + y = 6xy in) Find the equation of the tangent…

A:

Q: Find the derivatives of the function f(x) from the first principle  sin2x

A: Answer and explanation is given below...

Q: a) Prove that (arctan r 1+2 b) Using part(a), find the derivative of f (x)= arctan (208 )

A: Properties of derivative  f(g(x))=f'(g(x)) g'(x)ddxcosx=-sinxddxax=axloga

Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

A:

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Determine the derivative of the function y=arcsin 2x / 1+x2 at x=2.

A:

Q: Find the derivative of f(x) = arcsin 2

A:

Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: Find the derivative of the function.

A: fx=arc sinx + arc cosx

Q: FInd the derivative using implicit differentiation rules x2+y2=x+y

A:

Q: Find the derivative of the function.

A: Given: g(x)=arcsin(3x)x

Q: find the derivative. y = ecos−1 x

A: Given: y=ecos-1(x)

Q: Find y' by direct differentiation (with respect to x). y = 10etan(x) and y = (x3 + 4) sin(x)

A:

Q: find the derivative of y with respect to the appropriatevariable. y = ln (tan-1 x)

A: The given function is y=lntan-1x

Q: compute the derivative g(x) = tan−1(ln x)

A:

Q: Find the derivative of the function f(x) = arcsin x + arccos x

A:

Q: Compute the derivative of f(x) = arcsin(x? e

A: Given f(x)=sin-1(x2e3x)

Q: е. у %3D Arcsin (1 — 2x) f. y = x² In x

A: topic - derivatives

Q: Find the derivative of the function.

A:

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

A:

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: Find the derivative of the function cos (x) using the definition

A: We have to find the derivative of cos (x) by using definition of derivative

Q: Find the derivative of the function. Simplify where possible. y   =arctan(cos θ)

A: Given:y=arc tancosθFormula:ddxtan-1u=11+u2.dudx

Q: Using the Chain Rule, compute the first derivative of sin 1–x.

A: chain rule Let f(x) = g(h(x)) And let u = h(x) Using the above, function f may be written as: f(x) =…

Q: Find y" by implicit differentiation.   x3 + y3 =1

A: We find y' first

Q: Determine the second derivative of the function y=arcsin x2−1 / x2+1.

A:

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

A:

Q: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: Find the second derivative of the implicitly defined function x2+y2=R2 (canonical equation of a…

A: Given function is Differentiating both sides with respect to x, we get

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 1. y = Arcsin(- Vx²+4

A:

Q: Use logarithmic differentiation to find the derivative of y. y= cos X-3x + %3D

A: We can find the derivative using logarithmic differentiation as below.

Q: 6. Find y"by implicit differentiation of x³ + y3 = 1.

A:

Q: Find the derivative of y with respect to x. y=ln(tan-1(4x5))

A:

Q: What is the derivative OF a Arcsin X y= 3

A:

Q: Find the derivative of y = (sin x)arcsin x %3D

A:

Q: Use the Chain Rule to find the derivative. y = tan(θ + cos θ)

A:

Q: What is the derivative of: y = x√arcsin x

A: