Question

find dy/dx if y =e^2x+log5x+log7x​

Answer 1

Question:

$y = {e}^{2x} + log5x + log7x$

Answer:

$diff \: w.r.t.x$

$\frac{dy}{dx} = {e}^{2x} \frac{d}{dx} (2x) + \frac{1}{5x} \frac{d}{dx} (5x) + \frac{1}{7x} \frac{d}{dx} (7x) \\ \\ \frac{dy}{dx} = {e}^{2x} (2) + \frac{1}{5x} (5) + \frac{1}{7x} (7) \\ \\ \frac{dy}{dx} = 2 {e}^{2x} + \frac{1}{x} + \frac{1}{x}$

Formulae used:

$\star \: \frac{d( {e}^{x} )}{dx} = {e}^{x} \\ \\ \star \: \frac{d(logx)}{dx} = \frac{1}{x}$