What is the derivative of (cos(12x)/(e^{7x)}) ?

The derivative of (cos(12x)/(e^{7x)}) is -(12sin(12x)+7cos(12x))/(e^{7x)}

What is the first derivative of (cos(12x)/(e^{7x)}) ?

The first derivative of (cos(12x)/(e^{7x)}) is -(12sin(12x)+7cos(12x))/(e^{7x)}

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{cos ( 12 x )}{e ^{7 x}})

- \frac{12 sin ( 12 x ) + 7 cos ( 12 x )}{e ^{7 x}}

Solution steps

\frac{d}{d x} (\frac{cos ( 12 x )}{e ^{7 x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( 12 x ) ) e ^{7 x} - \frac{d}{d x} ( e ^{7 x} ) cos ( 12 x )}{( e ^{7 x} ) ^{2}}

\frac{d}{d x} (cos (12 x)) = - sin (12 x) \cdot 12

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= \frac{( - sin ( 12 x ) \cdot 12 ) e ^{7 x} - e ^{7 x} \cdot 7 cos ( 12 x )}{( e ^{7 x} ) ^{2}}

Simplify

\frac{( - sin ( 12 x ) \cdot 12 ) e ^{7 x} - e ^{7 x} \cdot 7 cos ( 12 x )}{( e ^{7 x} ) ^{2}} : - \frac{12 sin ( 12 x ) + 7 cos ( 12 x )}{e ^{7 x}}

= - \frac{12 sin ( 12 x ) + 7 cos ( 12 x )}{e ^{7 x}}

\int \frac{sec ^{6} ( x )}{tan ^{2} ( x )} d x

9 t - 2 t^{2}

\int 4 x^{- 2} d x

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

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

What is the derivative of (cos(12x)/(e^{7x)}) ?
The derivative of (cos(12x)/(e^{7x)}) is -(12sin(12x)+7cos(12x))/(e^{7x)}
What is the first derivative of (cos(12x)/(e^{7x)}) ?
The first derivative of (cos(12x)/(e^{7x)}) is -(12sin(12x)+7cos(12x))/(e^{7x)}