Question

Найдите производную функции: у=2ctgx-3x^8+x y=3*2^x-3/x^4+2 y=3sinx+1/x^3+2√x y=3ctgx-3x^8+5 y=2e^x+2/√x

Answer 1

1
$y=2ctgx-3x^8+x$
$y`=-2/sin^2x-24x^7+1$
2
$y=3*2^x-3/x^4+2$
$y`=3*2^x*ln2+12/x^5$
3
$y=3sinx+1/x^3+2 \sqrt{x}$
$y`=3cosx-3/x^4+1/ \sqrt{x}$
4
$y=3ctgx-3x^8+5$
$y`=-3/sin^2x-24x^7$
5
$y=2e^x+2/ \sqrt{x} \sqrt{x}$
$y`=2e^x-1/ \sqrt{x^3}$

Answer 2

$1)\; \; y=2ctgx-3x^8+x\\\\y'=- \frac{2}{sin^2x} -24x^7+1\\\\2)\; \; y=3\cdot 2^{x}-\frac{3}{x^4}+2\\\\y'=3\cdot 2^{x}\cdot ln2+\frac{3\cdot 4x^3}{x^8}=3\cdot 2^{x}\cdot ln2+ \frac{12}{x^5} \\\\3)\; \; y=3sinx+ \frac{1}{x^3}+2\sqrt{x}\\\\y'=3cosx-\frac{3x^2}{x^6} + \frac{2}{2\sqrt{x}} =3cosx- \frac{3}{x^4}+ \frac{1}{\sqrt{x}} \\\\4)\; \; y=3ctgx-3x^8+5\\\\y'=- \frac{3}{sin^2x}-24x^7\\\\5)\; \; y=2e^{x}+\frac{2}{\sqrt{x} }\\\\y'=2e^{x}-\frac{2\cdot \frac{1}{2\sqrt{x}}}{x}=2e^{x}- \frac{1}{\sqrt{x^3}}$