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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derivative of

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)

ln (x) - x^{2} y = x y^{^{'}}

\int_{1}^{4} \frac{5}{x} d x

\frac{d}{d x} (\frac{x}{2} - ln (3))

\frac{d x}{d t} = - a x

\int_{3}^{7} \frac{x}{x ^{2} - 2} d 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)