By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx (0.=) = 2.find a dt e(x²+5x) sin y 8+cos*(2nt)

Q: Find ay dt + = -1 (+-√e ³ sin ¹ (2+) 1(5+2log +) 9

A: We will use the formula ddtmn=nm'-mn'n2

Q: 6. Find dy dx of cos y - 2xy + 3x = 2x sin x

A:

Q: Show that (a) · J-1;2(x) = 2 Vлx cos x

A:

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

A:

Q: Differential Calculus Find the third derivative of the ff: 1) y x 1-ex 2) y = 2ex - 8x 3) y = 6ex -…

A: We have to find the third derivative of the given function.

Q: Show that Loo (1 COS X (1+x²)² dx кіо π e

A:

Q: dy (1M1) Find dx 70x9 1+ 5x = sin(xcy²) I

A:

Q: Let g(x) = f() dt, v %3D

A:

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

A:

Q: Evaluate 4x³ sin² (x¹) dx + C

A:

Q: 6. Find the derivatives of the following: a) g(r) = sin(vi) dt %3D g(=) = /" Ve +4 dt

A: Please refer to the image below

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

A:

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

A:

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

A:

Q: If g(x) = | cos' t dt , then determine g'(x). %3D

A:

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

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 the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: satisfied

A: We will solve the problem.

Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: S cos 4x cos 3x dx

A: Given: I=∫cos(4x)cos(3x)dx