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

The derivative of x^2cos(1/(x^2)) is 2xcos(1/(x^2))+(2sin(1/(x^2)))/x

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

The first derivative of x^2cos(1/(x^2)) is 2xcos(1/(x^2))+(2sin(1/(x^2)))/x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

x \to - 2 lim (\frac{x + 1}{x + 2})

y = x, y = 0, x = 25

y^{^{'}} + 2 y = 3 x

7 x + 4

\int_{1}^{2} (x - 1)^{2} d x

What is the derivative of x^2cos(1/(x^2)) ?
The derivative of x^2cos(1/(x^2)) is 2xcos(1/(x^2))+(2sin(1/(x^2)))/x
What is the first derivative of x^2cos(1/(x^2)) ?
The first derivative of x^2cos(1/(x^2)) is 2xcos(1/(x^2))+(2sin(1/(x^2)))/x