What is the derivative of y=(cos(x))/(x^5) ?

The derivative of y=(cos(x))/(x^5) is -(xsin(x)+5cos(x))/(x^6)

What is the first derivative of y=(cos(x))/(x^5) ?

The first derivative of y=(cos(x))/(x^5) is -(xsin(x)+5cos(x))/(x^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = \frac{cos ( x )}{x ^{5}}

- \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) cos ( x )}{( x ^{5} ) ^{2}}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{( - sin ( x ) ) x ^{5} - 5 x ^{4} cos ( x )}{( x ^{5} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{5} - 5 x ^{4} cos ( x )}{( x ^{5} ) ^{2}} : - \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

= - \frac{x sin ( x ) + 5 cos ( x )}{x ^{6}}

What is the derivative of y=(cos(x))/(x^5) ?
The derivative of y=(cos(x))/(x^5) is -(xsin(x)+5cos(x))/(x^6)
What is the first derivative of y=(cos(x))/(x^5) ?
The first derivative of y=(cos(x))/(x^5) is -(xsin(x)+5cos(x))/(x^6)