Question

Найти производную функции y = 5x^2 - 2/√x + sin π/4

Answer 1

Ответ:

  $\boxed{\ (u\pm v)'=u'\pm v'\ \ ,\ \ (x^{n})'=nx^{n-1}\ ,\ (Cu)'=Cu'\ ,\ \ \Big(\frac{u}{v}\Big)'=\frac{u'v-uv'}{v^2}\ ,\ C'=0\ }$

$y=5x^2-\dfrac{2}{\sqrt{x}}+sin\dfrac{\pi }{4}\ \ \Rightarrow \ \ \ y=5x^2-\dfrac{2}{\sqrt{x}}+\dfrac{\sqrt2}{2}\\\\\\y'=5\cdot 2x-\dfrac{-2\cdot(\sqrt{x})'}{(\sqrt{x})^2}+0=10x+\dfrac{2\cdot \frac{1}{2\sqrt{x}}}{x}=10x+\dfrac{1}{x\sqrt{x}}$