Problems from Derivative of a power

Development:

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

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

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

Solution:

a) $23x^{22}$

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

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

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