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

The derivative of x^2sin((2pi/x)) is 2xsin((2pi)/x)-2picos((2pi)/x)

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

The first derivative of x^2sin((2pi/x)) is 2xsin((2pi)/x)-2picos((2pi)/x)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = sin (\frac{2 π}{x})

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

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

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

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

Simplify

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

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

\int arcsec (x) d x

\int x^{-} d x

\frac{130700}{333 - v}

\int tan^{4} (\frac{3}{5} b x) d x

\frac{d}{d x} (in (sin (x)))

What is the derivative of x^2sin((2pi/x)) ?
The derivative of x^2sin((2pi/x)) is 2xsin((2pi)/x)-2picos((2pi)/x)
What is the first derivative of x^2sin((2pi/x)) ?
The first derivative of x^2sin((2pi/x)) is 2xsin((2pi)/x)-2picos((2pi)/x)