What is the derivative of (cos(x)/(x^6)) ?

The derivative of (cos(x)/(x^6)) is -(xsin(x)+6cos(x))/(x^7)

What is the first derivative of (cos(x)/(x^6)) ?

The first derivative of (cos(x)/(x^6)) is -(xsin(x)+6cos(x))/(x^7)

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\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{6}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{( - sin ( x ) ) x ^{6} - 6 x ^{5} cos ( x )}{( x ^{6} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{6} - 6 x ^{5} cos ( x )}{( x ^{6} ) ^{2}} : - \frac{x sin ( x ) + 6 cos ( x )}{x ^{7}}

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

What is the derivative of (cos(x)/(x^6)) ?
The derivative of (cos(x)/(x^6)) is -(xsin(x)+6cos(x))/(x^7)
What is the first derivative of (cos(x)/(x^6)) ?
The first derivative of (cos(x)/(x^6)) is -(xsin(x)+6cos(x))/(x^7)