12. Given the function f(x)= **)Cos(x) , find the value of the first derivative at x = 2 . sin(x) (a) Use analytical differentiation by hand. (b) Use the four-point central difference formula with x_2 = 1.96 , x¡-1 = 1.98 , x+1= 2.02 , and X;+2 = 2.04 . %3D

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

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

A:

Q: 10. Find the 87th derivative of y = cos(2x) at IT

A:

Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

A:

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

A:

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

A:

Q: 2) Let y = xe* and find the first derivative y'. Where is y'>0?What does this tell you about the…

A:

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

A:

Q: Find the indicated derivative of the function. for y = -4 cos X dx4

A:

Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: 4. Find the derivative of g(x) = e5" sin(-x). Do not simplify.

A:

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: а. h(x) —…

A: We need to find derivative.

Q: 4. Find the second derivative for the following functions: a) (ans.:6x +

A: Derivatives

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: 1. Find the derivative of the function sin (4x) f (x) = V 3x

A:

Q: MY The derivative with respect to x of the function y=-3tan-¹x-(In 3) log, (csc x) is y' = cotx + O…

A:

Q: f (x) = 1

A:

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

A:

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3.…

A:

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

A:

Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

Q: f(x) = x2 -1

A:

Q: 17) Find the derivative of y = x? COs x - 2

A:

Q: 5- When the first derivative of the y = sinx function at x =pi/4 is calculated with the forward…

A: We will use basics of numerical methods here

Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

A:

Q: 4 sin x-3 2. Find the first derivative of y =150xcos (10x)+ 9 In(J16-x)

A: use derivative of y

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

A:

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 dy dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE…

A: Given: x4y3=-8

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

A:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: (x² +SJ° In 14-X つ. dr

A:

Q: 1) Find the derivative of the given function with respects to 0 y = 3lan In 3

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

A:

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

A:

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

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

A:

Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx>1 Graph for this piecewise function is: B. Given function…

Q: 1.) f(x) = (2x + 1)(3x – 2)

A: