Question

f(x)=(3x^(3)+5)*e^(2x^(2))

Answer 1

$\text{Given the function $f(x)=(3x^{3}+5)*e^{2x^{2}}$}\\ \text{We find the derivative of f(x) using product rule}\\ \text{Let $u = 3x^{3}+5$ and $v = e^{2x^{2}}$ }\\ \text{Hence, $f'(x) = e^{2x^2} \cdot 9x^2 + (3x^3+5) \cdot 4xe^{2x^2}$}\\ f'(x) = e^{2x^2}(9x^2+12x^4+20x)$