What is the derivative of (-xsin(x)-cos(x))/(4x^2) ?

The derivative of (-xsin(x)-cos(x))/(4x^2) is -(x^2cos(x)+2(-xsin(x)-cos(x)))/(4x^3)

What is the first derivative of (-xsin(x)-cos(x))/(4x^2) ?

The first derivative of (-xsin(x)-cos(x))/(4x^2) is -(x^2cos(x)+2(-xsin(x)-cos(x)))/(4x^3)

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (\frac{- x sin ( x ) - cos ( x )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( - x sin ( x ) - cos ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{4} \cdot \frac{( - x cos ( x ) ) x ^{2} - 2 x ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( - x cos ( x ) ) x ^{2} - 2 x ( - x sin ( x ) - cos ( x ) )}{( x ^{2} ) ^{2}} : - \frac{x ^{2} cos ( x ) + 2 ( - x sin ( x ) - cos ( x ) )}{4 x ^{3}}

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

\int x^{2} - 6 x + 5 d x

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

y = 2 x^{3} - 2 x (- 1)

\frac{d}{d x} (2 cos (- 2 x))

\int \frac{34 x ^{2}}{( 2 x + 1 ) ( x ^{2} + 4 )} d x

What is the derivative of (-xsin(x)-cos(x))/(4x^2) ?
The derivative of (-xsin(x)-cos(x))/(4x^2) is -(x^2cos(x)+2(-xsin(x)-cos(x)))/(4x^3)
What is the first derivative of (-xsin(x)-cos(x))/(4x^2) ?
The first derivative of (-xsin(x)-cos(x))/(4x^2) is -(x^2cos(x)+2(-xsin(x)-cos(x)))/(4x^3)