Question $4$

$1$ pts

Consider the function $f(x)=e^{3x^4-3x^3}.$ To compute $f(x),$ we use the chain rule for $f(x)=e^{g(x)},$ where $g(x)=3x^4-3x^2.$

We express the derivative using the formula $f^{\text{'}}(x)=e^{s(x)}*g^{\text{'}}(x)=g^{\text{'}}(x)*e^{s(x)}.$ The derivative is

$f^{\text{'}}(x)=(12x^2-6x)e^{3x^2-3x^2}$

$f(z)=e^{12x^2-5c}$

$f^{\text{'}}(x)=12x^3-6x{e}^{3x^2-3x^2}$

$f^{\text{'}}(x)=(12x^2-6x)(3x^4-3x^2)$