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Popular >

derivative of 5xsin(pix)

Solution

\frac{d}{d x} (5 x sin (π x))

Solution

5 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (5 x sin (π x))

Take the constant out:

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

= 5 \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)

= 5 (\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

= 5 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 5 (sin (π x) + π x cos (π x))

Popular Examples

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\frac{d}{d x} (\frac{3000}{x + 3600 x ^{- 1}})

inverse oflaplace 9/(s(s^2+2s+9))inverse laplace

\frac{9}{s ( s ^{2} + 2 s + 9 )}

tangent of f(x)= 1/(x+1),(-2,-1)tangent of

f (x) = \frac{1}{x + 1}, (- 2, - 1)

derivative of (6x^2+7x^4)

\frac{d}{d x} ((6 x^{2} + 7 x)^{4})

maclaurin e^{x^2+x}maclaurin

e^{x^{2} + x}

Frequently Asked Questions (FAQ)

What is the derivative of 5xsin(pix) ?
The derivative of 5xsin(pix) is 5(sin(pix)+pixcos(pix))
What is the first derivative of 5xsin(pix) ?
The first derivative of 5xsin(pix) is 5(sin(pix)+pixcos(pix))