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

The derivative of x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2

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

The first derivative of x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2

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\frac{d}{d x} (x^{2} sin (π x))

2 x sin (π x) + cos (π x) π x^{2}

Solution steps

\frac{d}{d x} (x^{2} sin (π x))

Apply the Product Rule:

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

f = x^{2}, g = sin (π x)

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

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

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

= 2 x sin (π x) + cos (π x) π x^{2}

What is the derivative of x^2sin(pix) ?
The derivative of x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2
What is the first derivative of x^2sin(pix) ?
The first derivative of x^2sin(pix) is 2xsin(pix)+cos(pix)pix^2