Question

Найдите производную функции f(x)=3xe^4x-x^2/sin x

Answer 1

$f(x) = 3xe^{4x} - \dfrac{x^{2}}{\text{sin} \ x}$

$f'(x) = 3e^{4x} + 3xe^{4x} \ \cdotp 4 - \dfrac{2x \ \cdotp \text{sin} \ x - x^{2} \ \cdotp \text{cos} \ x}{\text{sin}^{2}x} =$

$= 3e^{4x} + 12xe^{4x} - \dfrac{2x \ \cdotp \text{sin} \ x - x^{2} \ \cdotp \text{cos} \ x}{\text{sin}^{2}x}$