Question

Find dy/dx of y = " class="latex-formula"> (x^2)

Answer 1

Step-by-step explanation:

$y = log_2 x^2 \\ \therefore y = \frac{log x^2}{log2}\\ (By\:change\:of\:base\:law) \\ \\ \therefore y = \frac{2log x}{log2}\\\\ differentiating \: both \: side \: w \: r \: t \: x. \\ \\ \frac{dy}{dx} = \frac{2}{log2} \bigg(\frac{d}{dx} log x \bigg) \\ \\ \therefore \frac{dy}{dx} = \frac{2}{log2} \bigg( \frac{1} {x} \times \frac{d}{dx} x \bigg) \\ \\ \therefore \frac{dy}{dx} = \frac{2}{log2} \bigg(\frac{1}{x} \times 1\bigg) \\ \\ \huge \red{ \boxed{\therefore \frac{dy}{dx} = \frac{2}{xlog2}}}$