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

Question

Evaluate each of the following. $\frac{\mathrm{d}}{\mathrm{d}x}\left[ x^2 \sqrt{x+2} \right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[ (3x + 5) \sqrt{x+4} \right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[ \frac{1}{4}x^4 \sqrt[4]{(x+1)^3} \right]$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[ (x-2)^{\frac{1}{3}} (2x-1)^{-2} \right]$

Accepted Answer

(i) $\dfrac{5x^2+8x}{2\sqrt{x+2}}$ (ii) $\dfrac{9x+29}{2\sqrt{x+4}}$ (iii) $\dfrac{x^3(19x+16)}{16\sqrt[4]{x+1}}$ (iv) $\dfrac{23-10x}{3(2x-1)^3\sqrt[3]{(x-2)^2}}$

Techniques of Differentiation - Product Rule

Techniques of Differentiation - Product Rule

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