What is the derivative of (0.9e^x/(tan(x))) ?

The derivative of (0.9e^x/(tan(x))) is 0.9(e^xcot(x)-e^xcsc^2(x))

What is the first derivative of (0.9e^x/(tan(x))) ?

The first derivative of (0.9e^x/(tan(x))) is 0.9(e^xcot(x)-e^xcsc^2(x))

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\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

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

Solution steps

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

Simplify

\frac{0.9 e ^{x}}{tan ( x )} : 0.9 e^{x} cot (x)

= \frac{d}{d x} (0.9 e^{x} cot (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.9 \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)

= 0.9 (\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)

= 0.9 (e^{x} cot (x) + (- csc^{2} (x)) e^{x})

Simplify

= 0.9 (e^{x} cot (x) - e^{x} csc^{2} (x))

What is the derivative of (0.9e^x/(tan(x))) ?
The derivative of (0.9e^x/(tan(x))) is 0.9(e^xcot(x)-e^xcsc^2(x))
What is the first derivative of (0.9e^x/(tan(x))) ?
The first derivative of (0.9e^x/(tan(x))) is 0.9(e^xcot(x)-e^xcsc^2(x))