Find the Total Differential of each of the following functions. 12. Vx2 + y2 13. (x2 – y2)3 - 14. sin-1 (2)

Q: 14. d dx - (2x − 3g(x))| x=4

A: x12345f′(x)35214g′(x)24315

Q: Find both partial derivatives дz ?х дz and for the equation exy + yz² = x³yz ду

A:

Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: 1 t3 4u p 1.A (p, t, u) pt2 u? 2. g(x, y, z) = V² +z=2 + sin(ry – x²)

A:

Q: 1 (a) y = Va2 -- csc(2x) + 3 +1' (b) y = sin x

A: Compute the derivatives of the following functions (a) x2/3-cosec(2x)+1/π (b)( (x2+1)/sinx)3

Q: 12. a(t) a' (t) b(t) b'(t) -4 2 -3 -4 1 a. f(t) = a(t)b(t) Find f'(-4). b. g(t) = -3a(t)b(t) Find…

A:

Q: ф(x, y, z) = e-y.e-%+17

A:

Q: 3. 6. t ca)

A: The chain rule of differentiation is to be used to find the derivative of f(x)=(x3+x-1)3. The chain…

Q: at x= 1

A: 9). Given function is fx=2ex-x. To find derivative of the given function at x=1. Solution:…

Q: 2x Sin 1+x?

A: Evaluate the derivative of the given function as follows.…