What is the derivative of (sin(1/x)/(x^2)) ?

The derivative of (sin(1/x)/(x^2)) is (-cos(1/x)-2xsin(1/x))/(x^4)

What is the first derivative of (sin(1/x)/(x^2)) ?

The first derivative of (sin(1/x)/(x^2)) is (-cos(1/x)-2xsin(1/x))/(x^4)

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\frac{d}{d x} (\frac{sin ( \frac{1}{x} )}{x ^{2}})

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

Solution steps

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

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

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

= \frac{( - \frac{c o s ( \frac{1}{x} )}{x ^{2}} ) x ^{2} - 2 x sin ( \frac{1}{x} )}{( x ^{2} ) ^{2}}

Simplify

\frac{( - \frac{c o s ( \frac{1}{x} )}{x ^{2}} ) x ^{2} - 2 x sin ( \frac{1}{x} )}{( x ^{2} ) ^{2}} : \frac{- cos ( \frac{1}{x} ) - 2 x sin ( \frac{1}{x} )}{x ^{4}}

= \frac{- cos ( \frac{1}{x} ) - 2 x sin ( \frac{1}{x} )}{x ^{4}}

x \to - \infty lim (9)

\int (4 - 3 x)^{5} d x

x \to 2 - lim (arcsin (\frac{x}{2}))

\frac{4}{5 s + 1}

\int ln ∣ 1 + x ∣ d x

What is the derivative of (sin(1/x)/(x^2)) ?
The derivative of (sin(1/x)/(x^2)) is (-cos(1/x)-2xsin(1/x))/(x^4)
What is the first derivative of (sin(1/x)/(x^2)) ?
The first derivative of (sin(1/x)/(x^2)) is (-cos(1/x)-2xsin(1/x))/(x^4)