Question

hw 12 - higher order derivatives section 2.7: problem 3 (1 point) calculate the second and third derivatives. $y = x^{4}-7x^{2}+x$ $y=square$ $y=square$

Explanation:

Step1: Find the first - derivative

Using the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, for $y=x^{4}-7x^{2}+x$, we have $y'=\frac{d}{dx}(x^{4}-7x^{2}+x)=4x^{3}-14x + 1$.

Step2: Find the second - derivative

Differentiate $y'$ with respect to $x$. Using the power rule again, $y''=\frac{d}{dx}(4x^{3}-14x + 1)=12x^{2}-14$.

Step3: Find the third - derivative

Differentiate $y''$ with respect to $x$. Using the power rule, $y'''=\frac{d}{dx}(12x^{2}-14)=24x$.

Answer:

$y'' = 12x^{2}-14$
$y''' = 24x$