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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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