Question

Математика!!!!!!!!!!!

Answer 1

Пошаговое объяснение:

$\displaystyle (u+v)'=u'+v'\\\\(x^n)'=nx^{n-1}$

a)

$\displaystyle y=4x^{17}+4\sqrt[5]{x^8}-\frac{1}{x^9}+\sqrt[4]{19}=\\\\=4x^{17}+4x^{\frac{8}{5} }-x^{-9}+\sqrt[4]{19}$

$\displaystyle y'=4*17x^{16}+4*\frac{8}{5} x^{\frac{3}{5} }-(-9)x^{-10}+0=\\\\=68x^{16}+\frac{32}{5} \sqrt[5]{x^3} +\frac{9}{x^{10}}$

б)

$\displaystyle (uv)'=u'v+uv'\\\\(tgx)'=\frac{1}{cos^2x}$

$\displaystyle y=(\sqrt{x^3}-7)tgx=(x^{\frac{3}{2} } -7)*tgx$

$\displaystyle y'=\frac{3}{2}x^{\frac{1}{2} } *tgx+(x^{\frac{3}{2} }-7)*\frac{1}{cos^2x} =\\\\=\frac{3\sqrt{x}* tgx}{2}+ \frac{x\sqrt{x} -7}{cos^2x}$