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Popular Calculus >

derivative of 9xsin(pix)

Solution

\frac{d}{d x} (9 x sin (π x))

Solution

9 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (9 x sin (π x))

Take the constant out:

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

= 9 \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)

= 9 (\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

= 9 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 9 (sin (π x) + π x cos (π x))

Graph

Popular Examples

limit as x approaches 1 of (x^6-1)/(x-1)

x \to 1 lim (\frac{x ^{6} - 1}{x - 1})

integral from 0 to 1 of 9/(x^5)

\int_{0}^{1} \frac{9}{x ^{5}} d x

integral of 1/((x^2-6x+11)^2)

\int \frac{1}{( x ^{2} - 6 x + 11 ) ^{2}} d x

derivative of y=-8^{5x^2-4}

d er i v a t i v e y = - 8^{5 x^{2} - 4}

limit as x approaches-1 of 3x^4-2x^3+4x

x \to - 1 lim (3 x^{4} - 2 x^{3} + 4 x)

Frequently Asked Questions (FAQ)

What is the derivative of 9xsin(pix) ?
The derivative of 9xsin(pix) is 9(sin(pix)+pixcos(pix))
What is the first derivative of 9xsin(pix) ?
The first derivative of 9xsin(pix) is 9(sin(pix)+pixcos(pix))