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Popular >

derivative of x^3cos(4x)

Solution

derivative of

x^{3} cos (4 x)

Solution

3 x^{2} cos (4 x) - 4 x^{3} sin (4 x)

Solution steps

\frac{d}{d x} (x^{3} cos (4 x))

Apply the Product Rule:

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

f = x^{3}, g = cos (4 x)

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

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

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

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

Simplify

= 3 x^{2} cos (4 x) - 4 x^{3} sin (4 x)

Popular Examples

integral of (tan^3(x))/(sec^6(x))

\int \frac{tan ^{3} ( x )}{sec ^{6} ( x )} d x

integral of sqrt(1-r^2)r

\int 1 - r^{2} r d r

limit as x approaches 4 of ln(x-4)

x \to 4 lim (ln (x - 4))

derivative of (ln(1+x)/((1-x)))

\frac{d}{d x} (\frac{ln ( 1 + x )}{( 1 - x )})

integral from 0 to 3 of 4x-x^2

\int_{0}^{3} 4 x - x^{2} d x

Frequently Asked Questions (FAQ)

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