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Popular >

derivative of 6xsin(pix)

Solution

\frac{d}{d x} (6 x sin (π x))

Solution

6 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (6 x sin (π x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \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)

= 6 (\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

= 6 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 6 (sin (π x) + π x cos (π x))

Graph

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\frac{d}{d x} (2 - \frac{1}{x})

integral of x/(sqrt(36-x^2))

\int \frac{x}{36 - x ^{2}} d x

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\int \frac{5 x ^{3} + 5 x}{x - 1} d x

d/(dt)(\sqrt[3]{t})

\frac{d}{d t} (3 t)

integral of x-1/2 sin(2x)

\int x - \frac{1}{2} sin (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 6xsin(pix) ?
The derivative of 6xsin(pix) is 6(sin(pix)+pixcos(pix))
What is the first derivative of 6xsin(pix) ?
The first derivative of 6xsin(pix) is 6(sin(pix)+pixcos(pix))