What is the derivative of (cos(x))/(x^8) ?

The derivative of (cos(x))/(x^8) is -(xsin(x)+8cos(x))/(x^9)

What is the first derivative of (cos(x))/(x^8) ?

The first derivative of (cos(x))/(x^8) is -(xsin(x)+8cos(x))/(x^9)

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derivative of

\frac{cos ( x )}{x ^{8}}

- \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{8}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{8} - \frac{d}{d x} ( x ^{8} ) cos ( x )}{( x ^{8} ) ^{2}}

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{( - sin ( x ) ) x ^{8} - 8 x ^{7} cos ( x )}{( x ^{8} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{8} - 8 x ^{7} cos ( x )}{( x ^{8} ) ^{2}} : - \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

= - \frac{x sin ( x ) + 8 cos ( x )}{x ^{9}}

y = 8 x sin (x)

\int_{0}^{0.5} 2 x d x

- 0.04 x^{2} - 0.8 x + 70

\int 1 + 4 t^{2} d t

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

What is the derivative of (cos(x))/(x^8) ?
The derivative of (cos(x))/(x^8) is -(xsin(x)+8cos(x))/(x^9)
What is the first derivative of (cos(x))/(x^8) ?
The first derivative of (cos(x))/(x^8) is -(xsin(x)+8cos(x))/(x^9)