Question

find the given higher - order derivative.
$f(x)=x^{3}-x^{3}/4,f^{(3)}(x)$
$f^{(3)}(x)=$

Explanation:

Step1: Recall power - rule for derivatives

The power - rule states that if $y = x^n$, then $y^\prime=nx^{n - 1}$. Given $f^\prime(x)=x^{3}-\frac{1}{4}x^{3}=\frac{3}{4}x^{3}$.

Step2: Find the second - derivative

Differentiate $f^\prime(x)=\frac{3}{4}x^{3}$ using the power - rule. $f^{\prime\prime}(x)=\frac{3}{4}\times3x^{2}=\frac{9}{4}x^{2}$.

Step3: Find the third - derivative

Differentiate $f^{\prime\prime}(x)=\frac{9}{4}x^{2}$ using the power - rule. $f^{(3)}(x)=\frac{9}{4}\times2x=\frac{9}{2}x$.

Answer:

$\frac{9}{2}x$