Find the derivative d/dx(x^(1/5)) using the power rule

 Exercise

\frac{d}{dx}\sqrt[5]{x}

 

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$ , then $f'(x) = nx^{n-1}$

\frac{1}{5}x^{\left(\frac{1}{5}-1\right)}

 

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$ , where $n$ is a number

\frac{1}{5}\frac{1}{x^{\left|-\frac{4}{5}\right|}}

 

Multiplying fractions $\frac{1}{5} \times \frac{1}{x^{\left|-\frac{4}{5}\right|}}$

\frac{1}{5x^{\left|-\frac{4}{5}\right|}}

 

Multiplying fractions $\frac{1}{5} \times \frac{1}{\sqrt[5]{x^{4}}}$

\frac{1}{5\sqrt[5]{x^{4}}}

\frac{1}{5\sqrt[5]{x^{4}}}

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.