Question

Найти производную функции 1)y=5(x+2)^5

2)y=1/корень x + 1

3)y=(x^2+1)^3​

Answer 1

1.

$y = 5 {(x + 2)}^{5}$

$y '= 5 \times 5 {(x + 2)}^{4} \times (x + 2)' = \\ = 25 {(x + 2)}^{ 4} \times 1 = 25 {(x + 2)}^{4}$

2.

$y = \frac{1}{ \sqrt{x + 1} } = {(x + 1)}^{ - \frac{1}{2} } \\$

$y' = - \frac{1}{2} {(x + 1)}^{ - \frac{3}{2} } \times (x + 1)' = \\ = - \frac{1}{2 \sqrt{ {(x + 1)}^{3} } }$

3.

$y = {( {x}^{2} + 1) }^{3}$

$y '= 3 {( {x}^{2} + 1) }^{2} \times ( {x}^{2} + 1)' = \\ = 3 {( {x}^{2} + 1) }^{2} \times 2x = 6x {( {x}^{2} + 1)}^{2}$