Evaluate each of the following. $\frac{\mathrm{d}}{\mathrm{d}x}\left[(x-1) \sqrt{2x+1}\right]$ \(\

Question

Evaluate each of the following. $\frac{\mathrm{d}}{\mathrm{d}x}\left[(x-1) \sqrt{2x+1}\right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[(2x-1)^{-3} \sqrt{1-3x^2}\right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[(3x-1)^3 \sqrt{1-2x^2}\right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[3x(x^3-9)^3\right]$

Accepted Answer

(i) $\dfrac{3x}{\sqrt{2x+1}}$ (ii) $\dfrac{12x^2+3x-6}{(2x-1)^4\sqrt{1-3x^2}}$ (iii) $\dfrac{(3x-1)^2(-24x^2+2x+9)}{\sqrt{1-2x^2}}$ (iv) $3(x^3-9)^2(10x^3-9)$

Techniques of Differentiation - Product Rule

Techniques of Differentiation - Product Rule

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