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Simplify $\sqrt[5]{n^{10}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $10$ and $n$ equals $\frac{1}{5}$
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$derivdef\left(n^{10\frac{1}{5}}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of n^10^1/5 using the definition. Simplify \sqrt[5]{n^{10}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 10 and n equals \frac{1}{5}. Multiply 10 times \frac{1}{5}. Find the derivative of n^{2} using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is n^{2}. Substituting f(x+h) and f(x) on the limit, we get. Expand the expression \left(n+h\right)^{2} using the square of a binomial: (a+b)^2=a^2+2ab+b^2.