a) f sin(x) cos(x) dx,

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

A:

Q: y = cos*x – sin*x

A: y = cos 4 x -  sin 4 x

Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: Find the derivative of the trigonometric function.

A: Given :           h(x) = sin 2x cos 2x   To find h'(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: Find the derivative of y=cos-1(5/x) with respect to x.

A: The given inverse trigonometric function is,

Q: Calculate the derivative of: '(14z) cos f(1) = sin (14x) r(e) =O

A: Given query is to find the the derivative of f(x).

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: . Find the derivative with respect to x: y = tan¬(Vx² –- 1) + csc¯²(x),x > 1

A: Given thaty=arctanx2-1+arccscx To find its derivative

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Find the derivative. х10 cos yt dt y = A. sin (x) B. cos (x$) – - 1 C. Cos (x*) D. 10x° cos (x°)

A: We know that

Q: • y= cos(a' + x')

A:

Q: Find the derivative of y=. =x²- 1 2 COS X

A: Given,  y=x2-12cos x

Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: Find the derivative of the function r=sin(θ3)cos(3θ) dr/dθ=?

A:

Q: Find the second derivative of F(t) = | sin(x) cos(2)d.r.

A:

Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

Q: What is the derivative of sin? x f(x) = with respect to x? COs x

A:

Q: Calculate the derivative of the following function. y= cos (6 sin x) dy %3D dx

A: Given that        The function is y= cos(6 sin x) Here we have to find dy/dx .

Q: b)Find the derivative of the function x cos (2x + 3y) = y sin x

A:

Q: Find the derivative of the following functions: y = In(sec x?) + tan-1(cosx) +4 tan x?

A:

Q: Calculate the derivative of the following functions y = sin (4 cos z)

A: Consider the provided function, y=sin4cosz Find the derivative of the function.

Q: Find the derivative of the given function. y = x² sin 'x+x cos 4x

A: For     y=fx gx    dydx=fx ddxgx+gxddxfx   This is the multiplication rule of derivative .

Q: Find the derivative of y with respect to x. y = In (tan -1(2x4)) dy %3D dx

A:

Q: Find the derivative f (t) = 1- cos t | a. 1 cos t - 1 sin t C. 1– cos t - t · sint (1 – cos t)? b.

A:

Q: Find the derivative of the function.

A:

Q: Find the 25th derivative of g (0) = cos(40 + a) where a is a real valued constant.

A: The given function is: g(θ)=cos(4θ+α)

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

A: We can find the derivative as below

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

A:

Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: ind the derivative of the 1. y x cos x

A:

Q: 2. Find the derivative of the function. y = e* In (sinæ)

A:

Q: Find the derivative of the (e) h(x) = e5 sin (Væ) + a° sec ()-

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the requested higher-order derivative for the given function. d?y of y = 3 sin(x) + x² cos(x)…

A: Using Derivatives.

Q: prove that if f = sin x the derivative is df = cos x. S dx %3D

A:

Q: Find the second derivative y “ of " of y = 5z +sin zcosz

A:

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

A:

Q: 3. Find the derivative y'(x) implicitly. cos?x + cos²y = cos (2x + 2y)

A:

Q: Find the first and second derivatives of the function. f (x) = In(cos x)

A: We will use the chain rule and quotient rule of differentiation to find the first derivative and the…

Q: Find the derivative of the function. y = a 3 + cos 3 x)

A: Given: y=a3+cos3x

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

A:

Q: Find the derivative: 1+e5 f(x) = = COS 1.

A: The given function is f(x)=cos1+e5x1-e8x

Q: Find the first derivative: y=sin( cos x)

A: The given equation is; y = sin( cos x )

Q: Find the derivative of the given function 1+ sin(3 f(x) = ( V + 1

A: To find the derivative of the given function  Use formula of  Derivative of u/v  = { u'v - u v' } /…

Q: Can you help me step by step?

A: Given function,

Q: Find the derivative of y = [A 0 tan Od0. sin x

A: Then substitute it in dy/dx and use chain rule Write the integral as two parts: