Answer to Question #286807 in Calculus for Mani

Question

Find dp/dq If P= q²+3/(q-1)³+(q+1)³

Answer 1

$p=q²+\frac{3}{(q-1)³}+(q+1)³$

Differentiate both sides of the equation

$\frac{dp}{dq}=\frac{d}{dq}(q²+\frac{3}{(q-1)³}+(q+3)³$

The derivative of p with respect to q is

$p'$ .

By the sum rule,

$\implies p'=\frac{d}{dq}(q²)+\frac{d}{dq}\frac{3}{(q-1)³}+\frac{d}{dq}(q+1)³$

Differentiating the right side of the equation

$p'=2q-\frac{9}{(q-1)⁴}+3(q+1)²$

$\implies \frac{dp}{dq}=2q-\frac{9}{(q-1)⁴}+3(q+1)²$