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

The derivative of x*sin(1/x) is sin(1/x)-(cos(1/x))/x

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

The first derivative of x*sin(1/x) is sin(1/x)-(cos(1/x))/x

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derivative of

x \cdot sin (\frac{1}{x})

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (\frac{1}{x})

= \frac{d x}{d x} sin (\frac{1}{x}) + \frac{d}{d x} (sin (\frac{1}{x})) x

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y = x^{3} - 11 x^{2} + 30 x, y = - x^{3} + 11 x^{2} - 30 x

f (x) = 3 - e^{- x}

\frac{d}{d x} (3 7 x)

ln (x)

\int e^{- x} 1 + \frac{1}{e ^{2 x}} d x

What is the derivative of x*sin(1/x) ?
The derivative of x*sin(1/x) is sin(1/x)-(cos(1/x))/x
What is the first derivative of x*sin(1/x) ?
The first derivative of x*sin(1/x) is sin(1/x)-(cos(1/x))/x