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Popular >

derivative of 7xsin(pix)

Solution

\frac{d}{d x} (7 x sin (π x))

Solution

7 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (7 x sin (π x))

Take the constant out:

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

= 7 \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)

= 7 (\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

= 7 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 7 (sin (π x) + π x cos (π x))

Popular Examples

derivative of (7x^2-14x+14e^x)

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

integral of 1/((x-1)(x-2)(x-3))

\int \frac{1}{( x - 1 ) ( x - 2 ) ( x - 3 )} d x

derivative of-(30/(x^4))

\frac{d}{d x} (- \frac{30}{x ^{4}})

integral of (1-2x^2+3x^3)

\int (1 - 2 x^{2} + 3 x^{3}) d x

integral of (ln(4x^2))/(sqrt(x))

\int \frac{ln ( 4 x ^{2} )}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 7xsin(pix) ?
The derivative of 7xsin(pix) is 7(sin(pix)+pixcos(pix))
What is the first derivative of 7xsin(pix) ?
The first derivative of 7xsin(pix) is 7(sin(pix)+pixcos(pix))