Derivative of a power

Find the derivative of the following functions:

a)$f (x) = x^{23}$

b)$f(x)=\sqrt{x^7}$

c)$f (x) =\sqrt[9]{x^4}$

a) The exponent is $23$. Therefore, $f'(x) =23x^{23-1}=23x^{22}$

b) $f(x)=\sqrt{x^7}=x^{7/2}$; In this case the exponent is $7/2$, and therefore $f'(x)=\dfrac{7}{2}x^{5/2}$.

c) $f(x)=\sqrt[9]{x^4}=x^{4/9}$. The exponent is $4/9$, and therefore $f'(x)=\dfrac{4}{9}x^{-5/9}=\dfrac{4}{9\sqrt[9]{x^5}}$.

a) $23x^{22}$

b) $\dfrac{7}{2}x^{5/2}$

c) $\dfrac{4}{9}x^{-5/9}=\dfrac{4}{9\sqrt[9]{x^5}}$