Question

find $\frac{d^{2}y}{dx^{2}}$.
$y = - 7x^{5}+1$
$\frac{d^{2}y}{dx^{2}}=square$

Explanation:

Step1: Find the first - derivative

Use the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. For $y=-7x^{5}+1$, $\frac{dy}{dx}=-7\times5x^{5 - 1}+0=-35x^{4}$.

Step2: Find the second - derivative

Differentiate $\frac{dy}{dx}=-35x^{4}$ again using the power rule. $\frac{d^{2}y}{dx^{2}}=-35\times4x^{4 - 1}=-140x^{3}$.

Answer:

$-140x^{3}$