Question

Помогите решить производную

Answer 1

$1)f(x)=\frac{2x-3}{x+1}\\\\f'(x)=\frac{(2x-3)'*(x+1)-(2x-3)(x+1)'}{(x+1)x^{2}}= \frac{2(x+1)-(2x-3)}{(x+1)^{2}}= \frac{2x+2-2x+3}{(x+1)^{2}}= \frac{5}{(x+1)^{2}} \\\\2)f(x)=7\sqrt[7]{x^{3}} =7x^{\frac{3}{7}}\\\\f'(x)=7*\frac{3}{7} x^{-\frac{4}{7}}=3* \frac{1}{\sqrt[7]{x^{4}} }= \frac{3}{\sqrt[7]{x^{4} }}$

$3)f(x)=log_{5}x\\\\f'(x)=\frac{1}{xln5} \\\\4)f(x)=\sqrt{4x-2}\\\\f'(x)=\frac{1}{2\sqrt{4x-2}}*(4x-2)'= \frac{4}{2\sqrt{4x-2}}= \frac{2}{\sqrt{4x-2}}$