What is the derivative of f(x)=(cos(x))/(x^7) ?

The derivative of f(x)=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)

What is the first derivative of f(x)=(cos(x))/(x^7) ?

The first derivative of f(x)=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{cos ( x )}{x ^{7}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}} : - \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

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

\int \frac{3 x ^{2} + 2}{x ^{3} + 2 x} d x

\frac{d y}{d x} - 3 y = \frac{y}{x}

\frac{d}{d x} ((x - y)^{10})

\int (x^{2} + 5) e^{2 x} d x

x \to 8 - lim (x^{2} + 5)

What is the derivative of f(x)=(cos(x))/(x^7) ?
The derivative of f(x)=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)
What is the first derivative of f(x)=(cos(x))/(x^7) ?
The first derivative of f(x)=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)