Differentiate each of the following with respect to $x$. $y = (2x^2 - 1)^{\frac{1}{5}}$ \(y = \s

Question

Differentiate each of the following with respect to $x$. $y = (2x^2 - 1)^{\frac{1}{5}}$ $y = \sqrt[3]{2x^3 + 8}$ $y = (3\sqrt{x} + 4x)^2$ $y = \sqrt{(3x^2 + 1)^3}$

Accepted Answer

(i) $\dfrac{4x}{5(2x^2-1)^{4/5}}$ (ii) $\dfrac{2x^2}{(2x^3+8)^{2/3}}$ (iii) $2(3\sqrt{x}+4x)\left(\dfrac{3}{2\sqrt{x}}+4\right)$ (iv) $9x\sqrt{3x^2+1}$

Techniques of Differentiation - Chain Rule

Techniques of Differentiation - Chain Rule

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