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Popular >

derivative of x^3cos(3x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

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

Simplify

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

Popular Examples

integral of (8e^{8y})/(6+e^{8y)}

\int \frac{8 e ^{8 y}}{6 + e ^{8 y}} d y

integral of (sqrt(2x^2-3))/(x^2)

\int \frac{2 x ^{2} - 3}{x ^{2}} d x

2x^2*(dy)/(dx)=piysin(pi/(2x))

2 x^{2} \cdot \frac{d y}{d x} = π y sin (\frac{π}{2 x})

limit as x approaches-2-of x^4+5

x \to - 2 - lim (x^{4} + 5)

area y=sin^2(x),y=0 area

y = sin^{2} (x), y = 0

Frequently Asked Questions (FAQ)

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