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

The derivative of (e^x/(sin(2x))) is e^xcsc(2x)-2e^xcot(2x)csc(2x)

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

The first derivative of (e^x/(sin(2x))) is e^xcsc(2x)-2e^xcot(2x)csc(2x)

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

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

Simplify

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

\int x (2 x^{2} + 3)^{4} d x

x \to 0 lim (\frac{sin ( x )}{- x})

\frac{d}{d y} (x^{\frac{y}{z}})

- sin (x^{2})

\int_{2}^{8} \frac{1}{2 x + 1} d x

What is the derivative of (e^x/(sin(2x))) ?
The derivative of (e^x/(sin(2x))) is e^xcsc(2x)-2e^xcot(2x)csc(2x)
What is the first derivative of (e^x/(sin(2x))) ?
The first derivative of (e^x/(sin(2x))) is e^xcsc(2x)-2e^xcot(2x)csc(2x)