Differentiation - Power Rule and Derivatives of Algebraic Functions

Differentiation - Power Rule and Derivatives of Algebraic Functions

Find the derivative of each of the following,

\(y = x^3\)
\(y = \frac{1}{x^7}\)
\(y = \frac{1}{\sqrt{x}}\)
\(y = \frac{x}{\sqrt[3]{x^5}}\)

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Answer:(a) \(3x^2\) (b) \(-7x^{-8}\) (c) \(-\frac{1}{2}x^{-\frac{3}{2}}\) (d) \(-\frac{2}{3}x^{-\frac{5}{3}}\)

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