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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (e^{x^{4} + x})

x^{2} + 3 x + 5

\frac{\partial}{\partial y} (x + 6 y)

\int x^{2} + 3 e^{x} + C d x

\frac{1}{1 - \frac{1}{1 - x}}

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