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Simplify $\sqrt[4]{x^8}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $8$ and $n$ equals $\frac{1}{4}$
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$derivdef\left(\frac{3x^2}{5x^{2}}\right)$
Learn how to solve problems step by step online. Find the derivative of (3x^2)/(5x^8^1/4) using the definition. Simplify \sqrt[4]{x^8} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 8 and n equals \frac{1}{4}. Simplify the fraction . Divide 3 by 5. Find the derivative of \frac{3}{5} 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 \frac{3}{5}. Substituting f(x+h) and f(x) on the limit, we get.