Question

Find the derivative of the given function.
f(x) = (x^1/4 + 11) (7 x^1/2+ 3)

Answer 1

21/4 x^-1/4 + 77/2 x^-1/2 + 3/4 x^-3/4.

Explanation:

Use the product rule;

d(uv) = udv/dx + v du/dx

u = x^1/4 + 11 and v = 7x^1/2+ 3.

f'(x) = (x^1/4 + 11)(7/2x^-1/2 + (7 x^1/2+ 3)1/4x^-3/4.

= 7/2x^-1/4 + 77/2x^-1/2 + 7/4x^-1/4 + 3/4x^-3/4

= 21/4 x^-1/4 + 77/2 x^-1/2 + 3/4 x^-3/4.

Answer 2

Explanation:

`f(x)=(x^{(1)/(4)}+11)(7 x^{(1)/(2)}+3)\\f'(x)=(x^{(1)/(4)}+11)(7*(1)/(2)x^{-(1)/(2)})+(1)/(4) x^{-(3)/(4)}(7 x^{(1)/(2)}+3)`