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Popular >

derivative of 3xsin(pix)

Solution

\frac{d}{d x} (3 x sin (π x))

Solution

3 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (3 x sin (π x))

Take the constant out:

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

= 3 \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)

= 3 (\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

= 3 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 3 (sin (π x) + π x cos (π x))

Popular Examples

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(\frac{x}{x ^{2} + 1})^{^{'}}

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\int_{- \infty}^{2} x e^{x} d x

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\frac{d}{d x} (6 x^{2} y - 3 x y^{2})

Frequently Asked Questions (FAQ)

What is the derivative of 3xsin(pix) ?
The derivative of 3xsin(pix) is 3(sin(pix)+pixcos(pix))
What is the first derivative of 3xsin(pix) ?
The first derivative of 3xsin(pix) is 3(sin(pix)+pixcos(pix))