. f(x) = sin(ln x)

Q: Find the derivative of the given function. f (x) = sin(ln x)

A: The given function is fx=sinlnx We have to find the derivative of this function.

Q: y = cos*x – sin*x

A: y = cos 4 x -  sin 4 x

Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

A:

Q: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: Find the first derivative of the given functions: 1.)  x=(Arcsinh(1-b))2   2.) y=e-xcosh ln(x)

A:

Q: Find the derivative of the function. f(x) = ln(5+e^x/5-e^x)

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: Find the derivative of  y=sin^-1(cos(x))

A: We can find the derivative as below

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

A:

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

A:

Q: y = ln 1-x² 1+x²

A:

Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: Determine the first derivative of the ff. function y = ln| le* – 1/

A: We have to find the first derivative of the function: y=lnexex-1 We know the property of logarithm,…

Q: find the second derivative of y=ln(e^x+e^-x)

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

Q: Find the derivative of the function.

A:

Q: 16. Use logarithmic differentiation to find y'. (a)= (x2 + 1)tan(=) (b) y = (sin (3z))VE

A:

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

A:

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 dx by using logarithmic differentiation for = (Cos x)(e)

A:

Q: Find the derivative of the function. sin(x) y = In(1 + 6v) dv cos(x)

A: Find the derivative of the following function

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: Find the derivatives of the functions y = ln cos-1 x

A: The given function is y=lncos-1x.

Q: Find the derivative of y=ln(cos(z))

A:

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: 54, y = (ln x)cos* cos x %3D

A:

Q: Differentiate the function y=ln(x5 sin2 x)

A:

Q: The nth derivative of y = sinx cosx

A: We know that,  2sinxcosx=sin2x Therefore, y=sinxcosxy=122sinxcosxy=12sin2x              ⋯⋯1…

Q: Find the indicated derivative. dz if z = In (x° + e4) dx dz dx

A: We can find the derivative as below

Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: What is the derivative of: y = ln ln(1 − cos x)

A:

Q: A-The derivative is y = In sin 0 cos 0 1+2 ln 0

A:

Q: (b) Find the derivative of y = log,(5x')+log, (sin.x)

A:

Q: Find the derivative of the function. f(0) = 3 ln(6)Pe

A:

Q: What is the derivative of: y = x ln cos x

A: The given function is   y = x ln cos x

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: The derivative of the function y = cos(x ln 3)log3 (sin x) is:

A:

Q: 11. In y = e" sin x

A:

Q: Find the derivative of the function x² ln 4y = y sin 4x + e2 Answer:

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Find the derivative of y with respect to x. 10) y = sin-1 (e6t)

A:

Q: Find dx * by implicit differentiation. r+y+ 4

A: x+y+xy=4d(x+y)dx+d(xy)dx=d(4)dx

Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative.

Q: Can i get help step by step?

A: Given,

Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

A:

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

A:

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: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx

Q: Can i get help step by step please

A: We have to use the power rule because of exponent -1 and then use the chain rule for (cscx-cotx).

Q: What is the derivative of : ln cos 3x

A: