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Popular >

derivative of 2xsin(2x)

Solution

\frac{d}{d x} (2 x sin (2 x))

Solution

2 (sin (2 x) + 2 x cos (2 x))

Solution steps

\frac{d}{d x} (2 x sin (2 x))

Take the constant out:

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

= 2 \frac{d}{d x} (x sin (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (2 x)

= 2 (\frac{d x}{d x} sin (2 x) + \frac{d}{d x} (sin (2 x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

Simplify

= 2 (sin (2 x) + 2 x cos (2 x))

Popular Examples

y^{''}+2y^'+10y=cos(t)+0.739

y^{^{''}} + 2 y^{^{'}} + 10 y = cos (t) + 0.739

derivative of f(x)=11x^3tan(x)derivative of

f (x) = 11 x^{3} tan (x)

derivative of (6x^2-12x+12e^x)

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})

integral of 1/(y^2-y)

\int \frac{1}{y ^{2} - y} d y

slope of f(x)=x^2+2 slope

f (x) = x^{2} + 2

Frequently Asked Questions (FAQ)

What is the derivative of 2xsin(2x) ?
The derivative of 2xsin(2x) is 2(sin(2x)+2xcos(2x))
What is the first derivative of 2xsin(2x) ?
The first derivative of 2xsin(2x) is 2(sin(2x)+2xcos(2x))