Question

Помогите найти производную функции.

Answer 1

$\frac{d}{dx} [(5x-x^{ \frac{1}{3} })(x- \frac{5}{x})$
$(5x-x^{ \frac{1}{3} }) \frac{d}{dx} [x- \frac{5}{x} ]+(x- \frac{5}{x} ) \frac{d}{dx} [5x-x{ \frac{1}{3} }]$
$(5x-x^{ \frac{1}{3} })(1+5x^{-2})+(x- \frac{5}{x} )(5-( \frac{1}{3}x^{ \frac{1}{3} -1}))$
$(5x-x^{ \frac{1}{3} })(1+5x^{-2})+(x- \frac{5}{x} )(5-( \frac{1}{3} x^{ \frac{1}{3} + \frac{-1}{1} \frac{3}{3} }))$
$(5x-x^{ \frac{1}{3} })(1+5x^{-2})+(x- \frac{5}{x} )(5-( \frac{1}{3}x^{ \frac{1}{3} + \frac{-1*3}{3}}))$
$(5x-x \frac{1}{3} )(1+5x^{-2})+(x- \frac{5}{x} )(5-( \frac{1}{3} \frac{x^{- \frac{2}{3}} }{1} }))$
$(5x-x^{ \frac{1}{3} })(1+5x^{-2})+(x- \frac{5}{x} )(5- \frac{x^{-\frac{2}{3}}}{3} )$
$(5x-x^{ \frac{1}{3} })(1+5 \frac{1}{ x^{2}})+(x- \frac{5}{x} )(5- \frac{x^{- \frac{2}{3}} }{3} )$
$(5x-x^{ \frac{1}{3}} )(1+5 \frac{1}{x^2} )+(x- \frac{5}{x} )(5- \frac{ \frac{1}{x^ \frac{2}{3} } }{3} })$
$(1+ \frac{5}{x^2} )(5x-x^{ \frac{1}{3} })+(5- \frac{1}{3x^{ \frac{2}{3} }} )(x- \frac{5}{x} )$