Question

Знайти похідну функцію y(x)
1)
$y = x$
2)
$y = - 3$
3)
$y = {x}^{6}$
4)
$y = \sqrt{x}$
5)
$y = \sqrt[3]{x}$
6)
$y = {x}^{ \frac{3}{4} }$
7)
$y = \cos(x)$
8)
$y = \tan(x)$
9)
$y = {x}^{ - 3}$
10)
$y = \sin(x)$
11)
$y = \cot(x)$
12)
$y = {3}^{x}$

Answer 1

1) y' = (x)' = 1
2) y'=(-3)' = 0
3) y'=(x^6)' = 6x^(6-1)=6x^5
4) y'=(sqrt(x))' = (x^(1/2))' = 1/2 * x^(1/2-1) = 1/2sqrt(x)
5) y'=(x^(1/3))' = 1/3 * x^(1/3-1) = 1/3 * x^(-2/3)
6) y' = (x^(3/4))' = 3/4 * x^(3/4-1) = 3/4 * x^(-1/4)
7) y' = -sinx
8) y'= 1/(1+x^2)
9) y' = -3*x^(-3-1) = -3*x^(-4) = -3/x^4
10) y' = cosx
11) y' = - 1/(1+x^2)
12) y' = 3^x * ln3