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

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

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

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

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derivative of

f (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}}

\int \frac{x}{4 - x ^{2}} d x

\frac{\partial}{\partial x} (11 x^{2} - 2 x^{3})

\int_{0}^{1} 2 π (x) (9 - 8 x - x^{2}) d x

g (x) = \frac{1 + 6 x}{9 - 4 x}

f^{^{'}} (x) = 3^{x}

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