find $\frac{d^{2}y}{dx^{2}}$.\n$y = - 7x^{5}+1$\n$\frac{d^{2}y}{dx^{2}}=square$
find $\frac{d^{2}y}{dx^{2}}$.\n$y = - 7x^{5}+1$\n$\frac{d^{2}y}{dx^{2}}=square$
Answer
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:
$-140x^{3}$