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

The derivative of (cot(x)/(e^x)) is -(csc^2(x)+cot(x))/(e^x)

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

The first derivative of (cot(x)/(e^x)) is -(csc^2(x)+cot(x))/(e^x)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( - csc ^{2} ( x ) ) e ^{x} - e ^{x} cot ( x )}{( e ^{x} ) ^{2}} : - \frac{csc ^{2} ( x ) + cot ( x )}{e ^{x}}

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

d er i v a t i v e 2 e^{x}

\int t sin^{2} (t) d t

x \to 0 lim (3 x^{2} - 5)

\int \frac{- 1}{1 + e ^{x}} d x

x \to - 5 lim (2 (- \frac{3}{10}) (x) - 3)

What is the derivative of (cot(x)/(e^x)) ?
The derivative of (cot(x)/(e^x)) is -(csc^2(x)+cot(x))/(e^x)
What is the first derivative of (cot(x)/(e^x)) ?
The first derivative of (cot(x)/(e^x)) is -(csc^2(x)+cot(x))/(e^x)