Question

If we differentiate the cost function: $y=\frac{x^4}{4}+2x^2$, we get

• A. $\frac{x^3}{4}+4x$
• B. $4x^3+4x$
• C. $x^3+4x$
• D. $4x^3+2x^2$

Answer 1

Answer: (C)

$x^3+4x$

Suppose: $y=a{x}^n$
Then, $dy=na{x}^{n-1}$
Remember
$\frac{x^4}{4}=\frac{1}{4}{x}^4$
So differentiating both terms in the expression for using the formula gives:
$\frac{dy}{dx}=x^3+4x$