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

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

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

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

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\frac{d}{d 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}}

\frac{d}{d x} ((5 x - 4)^{3})

\int x - 4 d x

\int e^{- x} \cdot x^{- 1} d x

\frac{d}{d x} (\frac{1}{9 + x ^{2}})

\frac{d}{d x} (x y e^{x y})

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