Question

how differentiate this question
(x^2-4)(x^2+3)^6

Answer 1

use product rule
\[\frac{d}{dx}(uv)=v \frac{du}{dx}+u \frac{dv}{dx}\]

Answer 2

\[\frac{d}{dx}(x^2-4)(x^2+3)^6=(x^2+3)^6 \frac{d}{dx}(x^2-4)+(x^2-4) \frac{d}{dx}(x^2+3)^6\]

Answer 3

= 2x (x²+3)^6 + 12x (x²-4) ( x² + 3) ^5
= 2x ( x² + 3) ^5 * [ x² + 3) + 6 (x²-4) ]
= 2x ( x² + 3) ^5 * ( 7x² - 21)