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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

h (x) = lo g_{10} (2 x^{2} + 5 x + 2)

(7 + x) y^{^{'}} + y = 7 + x

sec^{2} (x) - tan^{2} (x)

\frac{\partial}{\partial x} (\frac{x ^{4}}{6 y} + \frac{12 y ^{4}}{x})

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

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