What is the derivative of (cos(x)/(x^3)) ?

The derivative of (cos(x)/(x^3)) is -(xsin(x)+3cos(x))/(x^4)

What is the first derivative of (cos(x)/(x^3)) ?

The first derivative of (cos(x)/(x^3)) is -(xsin(x)+3cos(x))/(x^4)

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\frac{d}{d x} (\frac{cos ( x )}{x ^{3}})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{3}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Simplify

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

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

\int (x + 2 y + 3 z)^{2} d x

\int r^{2} - x^{2} d x

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

(19 x y^{2} + 11 y) + (19 x^{2} y + 11 x) (\frac{d y}{d x}) = 0

y^{^{''}} + 4 y = sec (2 x)

What is the derivative of (cos(x)/(x^3)) ?
The derivative of (cos(x)/(x^3)) is -(xsin(x)+3cos(x))/(x^4)
What is the first derivative of (cos(x)/(x^3)) ?
The first derivative of (cos(x)/(x^3)) is -(xsin(x)+3cos(x))/(x^4)