Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t) dt function by using Leibniz rule where F(x) = CB(x) a(x) %3D

Q: Find dy/dx by implicit differentiation   Cos(xy)  = 1  +Sin y

A: Differentiate both sides with respect to x. Using product rule and chain rule.

Q: 9. Find f' (x) for the function f (x) = sin? (cos(4x)) 10. Find f'(x) for the following functions:…

A: Given:          f(x) =sin2cos4x first derivative        ddxfx =f'x      f'x=ddxsin2cos4x    Applying…

Q: Differentiate the function. 8 + sin(t) f(t) cos(t) (a) f'(t) = Find f'(T). (b) f'(1) =

A: a:Here, f(t) =(8+sin(t))/cos(t)The derivative of f(t) is calculated as follows:

Q: Find f if f'(x) = sin x + cos x, f'(0) = 7, and f(0) = 7. Answer: f (x) =

A:

Q: Let h(y) = 20 cos y – 3 sin y. Then h'(y) =

A:

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: If f(x)- 3 cos 4x- - {).₁ 0 -3 -12 4 find f'

A:

Q: Solve the initial value problem dy/dx + 3¤y = f(x), y(0) = 1, f(x) = z²,0 1

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: If f(x) = 3e* cos(x), find f '(x) and f "(x). f '(x) = f "(x)

A:

Q: Let h(y) = 2 cos y – 7 sin y. Then h'(y) =

A:

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: Find f. f"(e) = sin(e) + cos(8), f(0) = 2, f(0) = 2 f(e) =

A: Given problem:- f''(θ) = sin(θ) + cos(θ) , f(0) =2 , f'(0) =2  To find:- f(θ)

Q: Find dy y= cof ( + tan)

A: Given : y = cot-12x+tan-1x2

Q: Find the value of f(0) when 3 sin(2t), f( f'(t) 1. f(0) 2. f (0) 3. f (0) 4. f(0) 5. f(0) = = = = =…

A:

Q: Find by implicit differentiation: dx a. cos y =x+ y

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: If f(z)-6 tan , then find the value of f'(1) is 12 6 1 V2

A:

Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B.…

A: We are asked to find the derivatives.

Q: Find df/dz.

A:

Q: Let f (x)  =  (tan−1(x))2. Find f '( 1/3).

A:

Q: (z2)juə = (x)/ sin(#x). Compute f'(x). %3D

A: We will solve the problem