Question

Differentiate: sqrt(x) * e^x^2 * (x^2 + 1)^10. Would the product rule work?

Answer 1

You'll have to use the product rule AND the chain rule for function composition.

Answer 2

\[\int\limits \frac{e^{x^2} \left(1+x^2\right)^9 \left(1+45 x^2+4 x^4\right)}{2 \sqrt{x}} \, dx=e^{x^2} \sqrt{x} \left(1+x^2\right)^{10} \]