What is the derivative of (xcos(x-sin(x))/(6x^2)) ?

The derivative of (xcos(x-sin(x))/(6x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(6x^3)

What is the first derivative of (xcos(x-sin(x))/(6x^2)) ?

The first derivative of (xcos(x-sin(x))/(6x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(6x^3)

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\frac{d}{d x} (\frac{x cos ( x ) - sin ( x )}{6 x ^{2}})

- \frac{x ^{2} sin ( x ) + 2 ( x cos ( x ) - sin ( x ) )}{6 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x cos ( x ) - sin ( x )}{6 x ^{2}})

Take the constant out:

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

= \frac{1}{6} \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{1}{6} \cdot \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{1}{6} \cdot \frac{( - x sin ( x ) ) x ^{2} - 2 x ( x cos ( x ) - sin ( x ) )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{6} \cdot \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 ) )}{6 x ^{3}}

= - \frac{x ^{2} sin ( x ) + 2 ( x cos ( x ) - sin ( x ) )}{6 x ^{3}}

x^{2} ln (9 x)

\frac{d}{d x} (9 x^{2} + 5)

\int_{0}^{0.5} 8 x - \frac{1}{8} x d x

n = 2 \sum \infty \frac{3}{2 ^{n}}

\int 6 x^{2} - 3 x d x

What is the derivative of (xcos(x-sin(x))/(6x^2)) ?
The derivative of (xcos(x-sin(x))/(6x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(6x^3)
What is the first derivative of (xcos(x-sin(x))/(6x^2)) ?
The first derivative of (xcos(x-sin(x))/(6x^2)) is -(x^2sin(x)+2(xcos(x)-sin(x)))/(6x^3)