Question

If $y=(5x^3-4x^2-8x{)}^9$, find $\frac{dy}{dx}$.

Answer 1

$y={\left(5x^3-4x^2-8x\right)}^{9}differentiatew.rtox\frac{dy}{dx}=\frac{d{\left(5x^3-4x^2-8x\right)}^9}{dx}\Rightarrow \frac{dy}{dx}=9\left(5x^3-4x^2-8x\right)\frac{d\left(5x^3-4x^2-8x\right)}{dx}\Rightarrow \frac{dy}{dx}=9\left(5x^3-4x^2-8x\right)\left(15x^2-8x-8x\right)Ans\Rightarrow \frac{dy}{dx}=9\left[75x^5-4x^4-40x^3-60x^4+32x^3+32x^2-120x^3+64x^2+64x\right]\Rightarrow \frac{dy}{dx}=9\left[75x^5-100x^4-128x^3+90x^2+64x\right]$