Exercise
Find the derivative of the following function:
f(x)=\frac{3}{\sqrt[3]{x}}-\frac{4}{\sqrt{x^5}}
Final Answer
Solution
We simplify the function before differentiating:
f(x)=\frac{3}{\sqrt[3]{x}}-\frac{4}{\sqrt{x^5}}=
=3x^{-\frac{1}{3}}-4x^{-\frac{5}{2}}
Using Derivative formulas, we get the derivative:
f'(x)=3\cdot (-\frac{1}{3})x^{-\frac{4}{3}}-4\cdot (-\frac{5}{2})x^{-\frac{7}{2}}
One can simplify the derivative:
=-x^{-\frac{4}{3}}+10x^{-\frac{7}{2}}=
=-\frac{1}{\sqrt[3]{x^4}}+10\cdot\frac{1}{\sqrt{x^7}}
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