Question

Найти производные функций

Answer 1

Ответ:

решение на фотографии

Answer 2

$1); ; y=2x^4-frac{3}{x^3}+8sqrt[4]{x^3}+5\\y'=8x^3-3cdot (-3)cdot x^{-4}+8cdot frac{3}{4}cdot x^{-1/4}+0=8x^3+frac{9}{x^4}+frac{6}{sqrt[4]{x}}$

$2); ; y=x+e^{-x}cdot cos4x\\y'=1-e^{-x}cdot cos4x-4, e^{-x}cdot sin4x$

$3); ; y=dfrac{2-tgsqrt{x}}{sin(5x+3)}\\y'=dfrac{-frac{1}{cos^2sqrt{x}}cdot frac{1}{2sqrt{x}}cdot sin(5x+3)-(2-tgsqrt{x})cdot 5cos(5x+3)}{sin^2(5x+3)}=\\\=dfrac{-sin(5x+3)-10sqrt{x}cdot cos^2sqrt{x}cdot cos(5x+3)cdot (2-tgsqrt{x})}{2sqrt{x}cdot cos^2sqrt{x}cdot sin^2(5x+3)}$

$4); ; y=Big(x^4-ln(2x+1)Big)^3\\y'=3cdot Big(x^4-ln(2x+1)Big)^2cdot Big(4x^3-frac{2}{2x+1}Big)$

$5); ; y=sqrt{arcsin (frac{3}{x}+2sin(x^5))}\\y'=dfrac{1}{2sqrt{arcsin (frac{3}{x}+2sin(x^5))}}cdot dfrac{1}{sqrt{1-Big(frac{3}{x}+2sin(x^5)Big)^2}}cdot Big (-dfrac{3}{x^2}+2, cos(x^5)cdot 5x^4Big)$