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

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

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

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

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\frac{d}{d x} (x^{2} \cdot 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 x} (4 x^{\frac{5}{4}} + 2 x^{\frac{3}{2}} + 7 x)

e^{3 a - 2 b t}

\int \frac{4}{x ^{2} + 4 x + 8} d x

n = 1 \sum \infty \frac{3}{2 n + 3}

\int (5 e^{- 0.4 x}) d x

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