## Derivatives of functions with exponents

### Task number: 3013

Determine the derivatives of the functions

#### Variant 1

\( e^{\sqrt{x+1}} \)

#### Variant 2

\(xe^{\frac1x}+e^{-\sqrt x}\)

#### Variant 3

\( x^x\)

#### Variant 4

\( x^{\sqrt x}\)

#### Variant 5

\( x^{\frac1x}\)

#### Variant 6

\( x^{\ln x}\)

#### Variant 7

\(\displaystyle \left(\frac{x}{x+1}\right)^x \)

#### Variant 8

\( (x^2+1)^{\sin x} \)

#### Variant 9

\( (\sin x)^{\cos x} \)