What is the derivative of xsin(pix) ?

The derivative of xsin(pix) is sin(pix)+pixcos(pix)

What is the first derivative of xsin(pix) ?

The first derivative of xsin(pix) is sin(pix)+pixcos(pix)

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\frac{d}{d x} (x sin (π x))

sin (π x) + π x cos (π x)

Solution steps

\frac{d}{d x} (x sin (π x))

Apply the Product Rule:

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

f = x, g = sin (π x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (π x) + cos (π x) π x

Simplify

= sin (π x) + π x cos (π x)

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

\int (cos (x) + 5^{x}) d x

\int (x^{2} + 6 x) cos (x) d x

\frac{d}{d x} (e^{a x^{6}})

d er i v a t i v e f (x) = (x)^{3} \cdot e^{(3 x)}

What is the derivative of xsin(pix) ?
The derivative of xsin(pix) is sin(pix)+pixcos(pix)
What is the first derivative of xsin(pix) ?
The first derivative of xsin(pix) is sin(pix)+pixcos(pix)