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

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

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

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

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

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

Solution steps

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

Simplify

\frac{e ^{x}}{tan ( x )} : e^{x} cot (x)

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

ln (x 2 - x)

\frac{d}{d x} (- cos (π x))

t^{2} y^{^{'}} + 4 t y - y^{3} = 0

x^{2}, 9 + x

\int csc^{2} (t) - 2 e^{t} d t

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