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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

t^{^{'}}

\frac{\partial}{\partial x} (\frac{3 x}{4})

\frac{d y}{d x} = k y

f (x) = 4 - 3 x^{2}, (- 2, - 8)

\int_{- π}^{π} cos^{2} (7 x) d x

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