Diffrentiate the following w.r.t.x x 7-3 x - Vidyadip

Question

Diffrentiate the following w.r.t.x

$\frac{x}{\sqrt{7-3 x}}$

✓

Answer

Let $y =\frac{x}{\sqrt{7-3 x}}$

Differentiating w.r.t. x, we get

$\begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}\left(\frac{x}{\sqrt{7-3 x}}\right)=\frac{\sqrt{7-3 x} \cdot \frac{d}{d x}(x)-x \frac{d}{d x}(\sqrt{7-3 x})}{(\sqrt{7-3 x})^2} \\ & =\frac{\sqrt{7-3 x} \times 1-x \times \frac{1}{2 \sqrt{7-3 x}} \cdot \frac{d}{d x}(7-3 x)}{7-3 x} \\ & =\frac{\sqrt{7-3 x}-\frac{x}{2 \sqrt{7-3 x}}(0-3 \times 1)}{7-3 x} \\ & =\frac{2(7-3 x)+3 x}{2(7-3 x)^{\frac{3}{2}}}=\frac{14-6 x+3 x}{2(7-3 x)^{\frac{3}{2}}}=\frac{14-3 x}{2(7-3 x)^{\frac{3}{2}}}\end{aligned}$

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