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

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

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

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

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\frac{d}{d x} (\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}}

\int sin^{5} (t) cos^{7} (t) d t

\frac{d}{d x} (arctanh (3 x))

ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

\int x - 25 - x^{2} d x

\frac{\partial}{\partial x} (2 x^{4} + 3 y^{3} + 2 x y)

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