If u = f(x3), v = g(x2), f ′(x) = cos x and g ′(x) = sin x,... | MATH - DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS | SolveeIt | Solveeit

Today, August 18

Question

If u = f(x³), v = g(x²), f ′(x) = cos x and

g ′(x) = sin x, then $\frac{du}{dv}$ is

A

$\frac{3}{2}$ x cos x³ . cosec x²

B

$\frac{2}{3}$ sin x³ . sec x²

C

tan x

D

None of these

Answer

$\frac{3}{2}$ x cos x³ . cosec x²

Explanation

Solution

u = f(x³) ⇒ du/dx = f ′(x³) . 3x² = cosx³ . 3x²

v = g(x²) = dv/dx = g ′(x²) . 2x = sinx² . 2x

du/dv = 3x/2 cosx³. cosecx²