Question

найдите производную функции y= f(x) f(x) = 4^x^2 * lnx

Answer 1

$f(x)=4^{x^2}\cdot lnx\\\\f'(x)=(4^{x^2})'\cdot lnx+4^{x^2}\cdot (lnx)'=\\\\=4^{x^2}\cdot ln4\cdot lnx+4^{x^2}\cdot \frac{1}{x}=4^{x^2}\cdot (ln4\cdot lnx+\frac{1}{x})=4^{x^2}\cdot \Big (ln(x^{ln4})+\frac{1}{x}\Big )$