If $y = \frac{x + 2}{\sqrt{3x + 2}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Use your resu

Question

If $y = \frac{x + 2}{\sqrt{3x + 2}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Use your result from (a) to find $\displaystyle\displaystyle\int_{2}^{4} \frac{3x + 6}{2 \sqrt{(3x + 2)^3}} \mathrm{d}x$.

Accepted Answer

(a) $\dfrac{3x-2}{2(3x+2)^{3/2}}$. (b) $\dfrac{5\sqrt{14}}{21}-\dfrac{\sqrt2}{3}$, using $y'+4(3x+2)^{-3/2}$.

Techniques of Differentiation - Quotient Rule

Techniques of Differentiation - Quotient Rule

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