What is the derivative of (e^{2x})/(sin(3x)) ?

The derivative of (e^{2x})/(sin(3x)) is 2e^{2x}csc(3x)-3e^{2x}cot(3x)csc(3x)

What is the first derivative of (e^{2x})/(sin(3x)) ?

The first derivative of (e^{2x})/(sin(3x)) is 2e^{2x}csc(3x)-3e^{2x}cot(3x)csc(3x)

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derivative of

\frac{e ^{2 x}}{sin ( 3 x )}

2 e^{2 x} csc (3 x) - 3 e^{2 x} cot (3 x) csc (3 x)

Solution steps

\frac{d}{d x} (\frac{e ^{2 x}}{sin ( 3 x )})

Simplify

\frac{e ^{2 x}}{sin ( 3 x )} : e^{2 x} csc (3 x)

= \frac{d}{d x} (e^{2 x} csc (3 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x}, g = csc (3 x)

= \frac{d}{d x} (e^{2 x}) csc (3 x) + \frac{d}{d x} (csc (3 x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

= e^{2 x} \cdot 2 csc (3 x) + (- cot (3 x) csc (3 x) \cdot 3) e^{2 x}

Simplify

= 2 e^{2 x} csc (3 x) - 3 e^{2 x} cot (3 x) csc (3 x)

\int \frac{2 x}{3} d x

\int \frac{7 x ^{2}}{4 x - x ^{2}} d x

\int_{0}^{1} x 3 - x^{2} d x

f (x) = [1 + e^{x}] [ln (x)], at x = 1

f (x) = e^{x} cos (x)

What is the derivative of (e^{2x})/(sin(3x)) ?
The derivative of (e^{2x})/(sin(3x)) is 2e^{2x}csc(3x)-3e^{2x}cot(3x)csc(3x)
What is the first derivative of (e^{2x})/(sin(3x)) ?
The first derivative of (e^{2x})/(sin(3x)) is 2e^{2x}csc(3x)-3e^{2x}cot(3x)csc(3x)