Q.3 а. Using first principle develop a formula of finding AY AX when Y- {(X)+g(X) Z(X)

derivatives

Activity 6: Find the first and the second derivative of the following: 1. y = ecosx 2. y = sin³ (e)* 3. у %3D Зхе2х 4. y = e* – - ex 5. y = 1 ex +2

B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the derivative in its simplest form in terms of x and y. dx (b) Let z(x,y) = (x – y) e¯*Y. Show that Əz Əz - (x +y) z ду (c) Let f(x) = x³ – 12x + 1. Find all the stationary points of f(x) and classify each of these stationary points as a local maximum, local minimum or neither.

show solution

Find the derivative of the function. 4х - 5 y =- 8x + 1 dx dx d (8х+ 1). — (4x - 5) - (4х — 5). dx d. (8x+ 1) dx y' = - (8x + 1)2 d d (8x + 1)• (4x - 5) – (4x- 5) • dx (8x+1) dx y' = - (4х - 5)2 d (8x + 1)• (4x- 5) + (4x - 5) • y' = - d (8x+ 1) dx dx (8x + 1)2 d. y' = (8x + 1) • (4x-5)- (4x-5) • (8x + 1) dx dx The solution is y' =

hyyfyff

derivatives

Q-1- Find the derivatives of the functionS 1-+In (xy)=!

3. Find the derivative y(15)of the function y = (x2 + x)sin(2x).