(a) the unit vector in the same direction as à = (1,2,2) (b) the gradient of h at P (c) the directional derivative of h at P in the direction of UA

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(7x/2) = 0 %3D %3D f(x)

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

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: Can you please solve this question?

A: we solve the question.please see 2nd step.

Q: II. Let F(r) = cos(3t – 1) dt. sin x 1. Find F(0). 2. Find F'(x).

A:

Q: A snake is crawling on a surface. The temperature at a point (x, y) is given by T(x, y) = 70 + 5…

A: We need to use toral derivative to find change in temperature

Q: Find f. f"(0) = sin(0) + cos(60), f(0) = 3, f'(0) = 1 f(0) = %3D

A:

Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

A:

Q: Find dy/dx at the point (0,1) using implicit differentiation given that xy + e y = e.

A: First we find dy/dx then put x=0 and y=1

Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

A:

Q: find dy/dt.

A:

Q: Find f. f(0) = f "(0) = sin(0) + cos(0), f(0) = 1, f(0) = 1, f'(0) = 3

A: Given that the expression

Q: 3) Is the function y(t)=cos(x(t)) linear or not?

A:

Q: Let a + 0 be a constant. Give an example of a function y = f(x) for which ay – y' = 0 and g?y – y" =…

A:

Q: dz If z = f(x, y) = x² + 2xy² and (x(t), y(t)) = (cos 2t, 2 sin t), use the Chain Rule to find…

A: We have to use the chain rule for finding the required derivative

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

A:

Q: dy BY IMPLICIT DIFFERENTIATION: 9x dx 1. FIND %3D secy

A: We have to find dydx by implicit differentiation: 9x=sec y We know the formula of differentiation,…

Q: chain

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.