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Popular >

derivative of 3x^2sin(4x)

Solution

\frac{d}{d x} (3 x^{2} sin (4 x))

Solution

3 (2 x sin (4 x) + cos (4 x) \cdot 4 x^{2})

Solution steps

\frac{d}{d x} (3 x^{2} sin (4 x))

Take the constant out:

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

= 3 \frac{d}{d x} (x^{2} sin (4 x))

Apply the Product Rule:

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

f = x^{2}, g = sin (4 x)

= 3 (\frac{d}{d x} (x^{2}) sin (4 x) + \frac{d}{d x} (sin (4 x)) x^{2})

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

= 3 (2 x sin (4 x) + cos (4 x) \cdot 4 x^{2})

Popular Examples

derivative of x^{-2cos(x})

\frac{d}{d x} (x^{- 2 c o s (x)})

limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x))

x \to 0 lim (\frac{( e ^{x} - e ^{- x} - 2 x )}{1 - sin ( x )})

limit as x approaches infinity of x*pi

x \to \infty lim (x \cdot π)

limit as x approaches infinity of 1/6

x \to \infty lim (\frac{1}{6})

y^{^{'}} = 1 + x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of 3x^2sin(4x) ?
The derivative of 3x^2sin(4x) is 3(2xsin(4x)+cos(4x)*4x^2)
What is the first derivative of 3x^2sin(4x) ?
The first derivative of 3x^2sin(4x) is 3(2xsin(4x)+cos(4x)*4x^2)