What is the derivative of (sin(x-x)/(x^3)) ?

The derivative of (sin(x-x)/(x^3)) is (2x+xcos(x)-3sin(x))/(x^4)

What is the first derivative of (sin(x-x)/(x^3)) ?

The first derivative of (sin(x-x)/(x^3)) is (2x+xcos(x)-3sin(x))/(x^4)

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\frac{d}{d x} (\frac{sin ( x ) - x}{x ^{3}})

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

Solution steps

\frac{d}{d x} (\frac{sin ( x ) - x}{x ^{3}})

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Simplify

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

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

x \to \infty lim (4 e^{x})

\int_{π}^{\infty} sin (x) d x

\frac{d}{d x} (16 e^{- 4 x})

\frac{d}{d x} (3 x ln (\frac{x}{2}))

\int 0.2 e^{- 0.2 x} d x

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