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Popular >

derivative of 3xsin(2x)

Solution

\frac{d}{d x} (3 x sin (2 x))

Solution

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

Solution steps

\frac{d}{d x} (3 x sin (2 x))

Take the constant out:

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

= 3 \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)

= 3 (\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

= 3 (1 \cdot sin (2 x) + cos (2 x) \cdot 2 x)

Simplify

= 3 (sin (2 x) + 2 x cos (2 x))

Popular Examples

derivative of 1/(4-x^2)derivative of

\frac{1}{4 - x ^{2}}

integral of (2sin(t)cos(t))

\int (2 sin (t) cos (t)) d t

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

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

limit as n approaches infinity of n!+n^3

n \to \infty lim (n! + n^{3})

y^{''}=4y,y^'(0)=1,y(0)=0

y^{^{''}} = 4 y, y^{^{'}} (0) = 1, y (0) = 0

Frequently Asked Questions (FAQ)

What is the derivative of 3xsin(2x) ?
The derivative of 3xsin(2x) is 3(sin(2x)+2xcos(2x))
What is the first derivative of 3xsin(2x) ?
The first derivative of 3xsin(2x) is 3(sin(2x)+2xcos(2x))