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Popular >

derivative of 2xsin(pix)

Solution

\frac{d}{d x} (2 x sin (π x))

Solution

2 (sin (π x) + π x cos (π x))

Solution steps

\frac{d}{d x} (2 x sin (π x))

Take the constant out:

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

= 2 \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)

= 2 (\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

= 2 (1 \cdot sin (π x) + cos (π x) π x)

Simplify

= 2 (sin (π x) + π x cos (π x))

Popular Examples

y^{''}-(3+pi)y^'+3pi*y=sin(pi/2)

y^{^{''}} - (3 + π) y^{^{'}} + 3 π \cdot y = sin (\frac{π}{2})

(x^2-9)y^'+6y=(x+3)^2

(x^{2} - 9) y^{^{'}} + 6 y = (x + 3)^{2}

derivative of x*sin(x^2)derivative of

x \cdot sin (x^{2})

tangent of x^2+xy-y^2=19,(4,1)tangent of

x^{2} + x y - y^{2} = 19, (4, 1)

limit as x approaches 0+of (cos(x)-1)/x

x \to 0 + lim (\frac{cos ( x ) - 1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 2xsin(pix) ?
The derivative of 2xsin(pix) is 2(sin(pix)+pixcos(pix))
What is the first derivative of 2xsin(pix) ?
The first derivative of 2xsin(pix) is 2(sin(pix)+pixcos(pix))