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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{sec ^{2} ( x ) - tan ( x )}{e ^{x}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

= \frac{sec ^{2} ( x ) e ^{x} - e ^{x} tan ( x )}{( e ^{x} ) ^{2}}

Simplify

\frac{sec ^{2} ( x ) e ^{x} - e ^{x} tan ( x )}{( e ^{x} ) ^{2}} : \frac{sec ^{2} ( x ) - tan ( x )}{e ^{x}}

= \frac{sec ^{2} ( x ) - tan ( x )}{e ^{x}}

x \to - 1 lim (\frac{x + 4}{2 x + 1})

x \to 0 lim (\frac{∣ x ∣ - x}{x})

\frac{d}{d x} (\frac{1}{tan ( x )})

\int \frac{cos ( x )}{4 - sin ^{2} ( x )} d x

\int (sec^{2} (x) - 7) d x

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