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

The derivative of x^2cos(pix) is 2xcos(pix)-pix^2sin(pix)

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

The first derivative of x^2cos(pix) is 2xcos(pix)-pix^2sin(pix)

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\frac{d}{d x} (x^{2} cos (π x))

2 x cos (π x) - π x^{2} sin (π x)

Solution steps

\frac{d}{d x} (x^{2} cos (π x))

Apply the Product Rule:

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

f = x^{2}, g = cos (π x)

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

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

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

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

Simplify

= 2 x cos (π x) - π x^{2} sin (π x)

\frac{d}{d x} (\frac{5}{x - 3})

\int - 4 cos (x) d x

\int_{0}^{2} e^{3 x} d x

\int (5 x^{4} - 3 x^{2} + 2 x + 6) d x

\int_{0}^{1} \frac{1}{v} d v

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