f(x)=x^3ln(2x^4+7)

please help me with this problem, thanks.

This requires the product and chain rules.

x^{3}\cdot\frac{8x^{3}}{2x^{4}+7}+3x^{2}ln(2x^{4}+ 7)

See what I done? The product rule is f(x)g'(x)+g(x)f'(x)

The derivative of ln(2x^{4}+7) requires the chain rule. That is essentially the

derivative of the inside times derivatives of outside.

Since the derivative of ln(u)=\frac{1}{u}, then we have

\frac{1}{2x^{4}+7}. But we multiply that by the derivative of the inside,

which is \frac{d}{dx}[2x^{4}+7]=8x^{3}

See? I will let you tidy it up.

Yes, that's it. Too bad, I wasn't here yesterday to answer before you!