Question

Найти производную 1) y=√x. 2) y=1/x. 3) y=1/√x 4)y=1/x^2. 5)y=8/4√x-6/3√x. 6)=x^2 sin x.

Answer 1

1) y'=(√x)' = $\frac{1}{2 \sqrt{x} }$
2) y'=(1/x)' =$-\frac{1}{ x^{2} }$
3) y'=(1/√x)' = $( x^{- \frac{1}{2} } )'=- \frac{1}{2} x^{ -\frac{3}{2} } = -\frac{1}{2 \sqrt{ x^{3} } }$
4) y'=(1/x^2)' =$( x^{-2} )' = -2 x^{-3} = - \frac{2}{x^{3} }$
5) y'= (8/4√x-6/3√x)' = (2√x-2√x)' = 0' = 0
6) y'=(x^2 sin x)' = 2x·sinx+ x²cosx.