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Popular >

derivative of x^3sin(2x)

Solution

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

Solution

3 x^{2} sin (2 x) + cos (2 x) \cdot 2 x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = sin (2 x)

= \frac{d}{d x} (x^{3}) sin (2 x) + \frac{d}{d x} (sin (2 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} sin (2 x) + cos (2 x) \cdot 2 x^{3}

Graph

Popular Examples

sum from n=1 to infinity}((3^{n+1 of))/((4^{n-1))}

n = 1 \sum \infty \frac{( 3 ^{n + 1} )}{( 4 ^{n - 1} )}

derivative of (600/(1+49(0.6)^x))

\frac{d}{d x} (\frac{600}{1 + 49 ( 0.6 ) ^{x}})

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\frac{d}{d x} (2 x + y^{2} - z^{2})

derivative of 10tan(x)

\frac{d}{d x} (10 tan (x))

d/(dX)(XY+YZ(Y+Z))

\frac{d}{d X} (X Y + Y Z (Y + Z))

Frequently Asked Questions (FAQ)

What is the derivative of x^3sin(2x) ?
The derivative of x^3sin(2x) is 3x^2sin(2x)+cos(2x)*2x^3
What is the first derivative of x^3sin(2x) ?
The first derivative of x^3sin(2x) is 3x^2sin(2x)+cos(2x)*2x^3