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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = sin (\frac{1}{x})

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

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

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

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

Simplify

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

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

\frac{d}{d y} (\frac{y}{x ^{2} + y ^{2}})

\int \frac{3 x ^{2}}{( x ^{3} + 1 ) ^{5}} d x

x \cdot e^{- A x}

\frac{d}{d x} (\frac{x}{( 2 x - 1 ) ^{6}})

\int (4 x + 3)^{3} d x

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