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

The derivative of (cos(x*e^x)/(tan(x))) is e^xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))e^x

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

The first derivative of (cos(x*e^x)/(tan(x))) is e^xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))e^x

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

\int cot^{2} (5 x) csc (5 x) d x

\frac{d}{d x} (arcsinh (1 - x^{2}))

\frac{d}{d x} (e^{- 2 t} cos (x))

\int a + b x d x

x \to 0 lim (\frac{3 ∣ x ∣}{x ^{2}})

What is the derivative of (cos(x*e^x)/(tan(x))) ?
The derivative of (cos(x*e^x)/(tan(x))) is e^xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))e^x
What is the first derivative of (cos(x*e^x)/(tan(x))) ?
The first derivative of (cos(x*e^x)/(tan(x))) is e^xcos(x)cot(x)+(-cos(x)-cot(x)csc(x))e^x