What is the derivative of (cos(x)/(x^8)) ?

The derivative of (cos(x)/(x^8)) is -(xsin(x)+8cos(x))/(x^9)

What is the first derivative of (cos(x)/(x^8)) ?

The first derivative of (cos(x)/(x^8)) is -(xsin(x)+8cos(x))/(x^9)

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 ( x )}{x ^{8}})

- \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{8}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{8} - \frac{d}{d x} ( x ^{8} ) cos ( x )}{( x ^{8} ) ^{2}}

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{( - sin ( x ) ) x ^{8} - 8 x ^{7} cos ( x )}{( x ^{8} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{8} - 8 x ^{7} cos ( x )}{( x ^{8} ) ^{2}} : - \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

= - \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

\frac{d}{d x} (\frac{1}{( 2 x + 3 ) ^{2}})

\int sin^{2} (x + 2) d x

\int 144 - t^{2} d t

\int_{0}^{5} (2 e^{x} + 4 cos (x)) d x

What is the derivative of (cos(x)/(x^8)) ?
The derivative of (cos(x)/(x^8)) is -(xsin(x)+8cos(x))/(x^9)
What is the first derivative of (cos(x)/(x^8)) ?
The first derivative of (cos(x)/(x^8)) is -(xsin(x)+8cos(x))/(x^9)