What is the derivative of (xcos(x-sin(x))/(x^2)) ?

The derivative of (xcos(x-sin(x))/(x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(x^3)

What is the first derivative of (xcos(x-sin(x))/(x^2)) ?

The first derivative of (xcos(x-sin(x))/(x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(x^3)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (30 x^{5} y^{4} - 20 x^{4} y^{3})

x \to - 2 lim (\frac{1}{x ^{2}})

x^{2} + y^{2} = 169, (12, - 5)

\frac{d}{d x} ((4 x - 13) ln ((2 x - 7) (x - 3)))

\int_{- 2}^{3} (8 z^{3} + 3 z - 1) d z

What is the derivative of (xcos(x-sin(x))/(x^2)) ?
The derivative of (xcos(x-sin(x))/(x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(x^3)
What is the first derivative of (xcos(x-sin(x))/(x^2)) ?
The first derivative of (xcos(x-sin(x))/(x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(x^3)