Question

Find dy/dx if y= e 3x ​log ( sin 2x )

Answer 1

Given y =e^3x log (sin2x) dy/dx= (e^3x × 1/sin2x ×cos 2x × 2) + log (sin 2x) × e^3x × 3

Answer 2

Answer:

The value of differential of given function is

$\frac{dy}{dx} = {e}^{3x} (2cot2x + 3log(sin2x))$

Step-by-step explanation:

The given equation is

$y = {e}^{3x} log( \sin2x )$

Differentiating it with respect to x we get

$\frac{dy}{dx} = {e}^{3x} \frac{d}{dx}(log(sin2x)) + log(sin2x) \frac{d}{dx} ( {e}^{3x} ) \\ = {e}^{3x} . \frac{1}{sin2x}.2cos2x + log(sin2x).(3 {e}^{3x} ) \\ = {e}^{3x} (2cot2x + 3log(sin2x))$

Therefore,the value if differential of given function is

$\frac{dy}{dx} = {e}^{3x} (2cot2x + 3log(sin2x))$

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