What is the derivative of (cos(x)/(x^4)) ?

The derivative of (cos(x)/(x^4)) is -(xsin(x)+4cos(x))/(x^5)

What is the first derivative of (cos(x)/(x^4)) ?

The first derivative of (cos(x)/(x^4)) is -(xsin(x)+4cos(x))/(x^5)

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\frac{d}{d x} (\frac{cos ( x )}{x ^{4}})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{4}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{( - sin ( x ) ) x ^{4} - 4 x ^{3} cos ( x )}{( x ^{4} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{4} - 4 x ^{3} cos ( x )}{( x ^{4} ) ^{2}} : - \frac{x sin ( x ) + 4 cos ( x )}{x ^{5}}

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

\frac{d}{d x} (\frac{y ^{2}}{x})

\frac{d}{d x} (ln (\frac{1}{3 x}))

\int sin (3 π) t d t

\frac{d}{d x} (3 e^{- x^{3}})

f (x) = x^{2} - 3 x + 1

What is the derivative of (cos(x)/(x^4)) ?
The derivative of (cos(x)/(x^4)) is -(xsin(x)+4cos(x))/(x^5)
What is the first derivative of (cos(x)/(x^4)) ?
The first derivative of (cos(x)/(x^4)) is -(xsin(x)+4cos(x))/(x^5)