6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In (1+sinx + cosx -1 b. g = xtan In Vx 1 c. h(x) = x° e

Q: cos ( bVx3 f(x) = a ln sin(cx²)

A:

Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

A:

Q: 1. Find the derivative of each function below. ex² - 3x +1 y = In(2e¬t sin t) A y =

A:

Q: Find the derivative of y with respect to the independent variable. COS y = 10 cos ( OA. -10 COS TO…

A:

Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

A:

Q: I Find the second derivative (y") of the following functions and simplify the final 1. y = x –…

A: As per our guideline, we are supposed to answer only the first question, to get remaining kindly…

Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

A:

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

A:

Q: 4. Determine the following derivatives without simplifying either before or after. d a. dx -…

A: As per the guidelines I am supposed to do the first three parts of a multipart question.  So I am…

Q: 7. Compute the derivative of y = tan-(Kr) 1. at the point r = K

A:

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 first and second derivative of y = e^−2x(cos3x+sin3x)

A: The first derivative of the given function by using the product rule of the derivative:

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: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: Derive the formula dy/dx= 1/ (1 + x2) for the derivative of y = tan-1 x by differentiating both…

A: Given,

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

A:

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

A:

Q: 3. Find the derivative y'(x) implicitly. cos²x + cos²y = = cos (2x +2y)

A:

Q: Given: f(x) = / (2 – 4t) sin() - dt %3D tan(2r) 17 – cos(2nt) Find the equation of the line tangent…

A: The tangent is a straight line to a curve that touches the curve at exactly one point. The point…

Q: Find the derivative of the given functions. 1. D;(x²cos 2x) 1 1 2. y =x + 7sin 2x 3. f(x) = sin?(5x…

A: We have to find

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

A:

Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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: 3. Use the Leibnitz formula for differentiation to find (i) for the function y=sin" xin) (ii) for…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

A:

Q: Evaluate the second derivative of mq4.5.png os (bVx³) f(x) = a ln sin(cx2) if a = 21, b = 0.5, and c…

A: Given that, f(x)=alncosbx3sincx2a=21, b=0.5, c=5Substituting the values of a, b and c, we…

Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

A:

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: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

A:

Q: Find the differential of the function. y=x^4 (sin(8x))

A: topic:-  derivatives

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

A:

Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

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: 1. Calculate the derivative of the following function. y= V2x + 19 dx 2. Calculate the derivative of…

A:

Q: 16. S(3 sin 0 + 5 cos 0)d0

A: A detailed solution is given below     ( As per our guidelines, i have to answer only 1st question…

Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

A:

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

A:

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: 1. Find the derivative of the following functions (dy/dx) at x=0 y= sin 2x – 2sec x 2. Find the…

A: We are given: y=sin 2x - 2 sec x and y = sin4 4x - cos4 4x We need to find their derivatives at…

Q: V=ln( cosn 92) %3D

A:

Q: Find the derivative of y with respect to the independent variable. 20) y = 7cos TO A) -17COS TO In 7…

A:

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

A:

Q: Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e…

A: We have to find