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Popular >

derivative of 4xsin(pix)

Solution

\frac{d}{d x} (4 x sin (π x))

Solution

4 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (4 x sin (π x))

Take the constant out:

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

= 4 \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)

= 4 (\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

= 4 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 4 (sin (π x) + π x cos (π x))

Popular Examples

tangent of f(x)=(x^2)/(x+8),\at x=2 tangent of

f (x) = \frac{x ^{2}}{x + 8}, at x = 2

integral of 10xln(9x)

\int 10 x ln (9 x) d x

integral from-pi to 0 of sin(x)

\int_{- π}^{0} sin (x) d x

derivative of ((x^2)/(x-1))

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

limit as x approaches 0 of (x^2-4x)/x

x \to 0 lim (\frac{x ^{2} - 4 x}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 4xsin(pix) ?
The derivative of 4xsin(pix) is 4(sin(pix)+pixcos(pix))
What is the first derivative of 4xsin(pix) ?
The first derivative of 4xsin(pix) is 4(sin(pix)+pixcos(pix))