Techniques of Differentiation - Chain Rule

Techniques of Differentiation - Chain Rule

Find the derivative of each of the following,

\(\mathrm{f}(x) = (2x^2 - 1)^5\)
\(y = \sqrt[3]{2x^3 - 8}\)
\(\mathrm{f}(x) = (2\sqrt{x} + 2x)^2\)

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Answer:(a) \(20x(2x^2-1)^4\) (b) \(2x^2(2x^3-8)^{-\frac{2}{3}}\) (c) \(2(2\sqrt{x}+2x)\left(\frac{1}{\sqrt{x}}+2\right)\)

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