Question

If y = 5x^3 - 4x² + 2 then value of d^2y/dx^2 at x = 1 is

(1) 22
(2) 7
(3) 24
(4) 3​

Answer 1

Answer:

Chain Rule of Differentiation

Let f(x) = (g o h)(x) = g(h(x))

Let u = h(x)

Using the above, function f may be written as:

f(x) = g(u)

the derivative of f with respect to x, f ' is given by:

f '(x) = (df / du) (du / dx)

Examples Using the Chain Rule of Differentiation

We now present several examples of applications of the chain rule.

Example 1

Find the derivative f '(x), if f is given by

f(x) = 4 cos (5x - 2)

Solution to Example 1

Let u = 5x - 2 and f(u) = 4 cos u, hence

du / dx = 5 and df / du = - 4 sin u

We now use the chain rule

f '(x) = (df / du) (du / dx) = - 4 sin (u) (5)

We now substitute u = 5x - 2 in sin (u) above to obtain

f '(x) = - 20 sin (5x - 2)

Answer 2

Answer:

22

Explanation:

Refer to the above explanation.