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.