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

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

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

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

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derivative of

f (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}}

x \to - 2 - lim (\frac{x - 3}{x ^{2} - 4})

\int sin (a x) cos (a) x d x

\frac{d}{d x} (x^{2} arctan (5 x) + ln (1 + 4 x^{2}))

\frac{d}{d x} (9 sin (4 x))

\frac{36}{( 1 + 3 x ) ^{3}}

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