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Popular >

derivative of x^3cos(x)

Solution

derivative of

x^{3} cos (x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral from 0 to pi/(12) of tsin(4t)

\int_{0}^{\frac{π}{12}} t sin (4 t) d t

sum from n=0 to infinity of 1/(n+12)

n = 0 \sum \infty \frac{1}{n + 12}

(\partial)/(\partial x)(4x^2y-2x+2y^3)

\frac{\partial}{\partial x} (4 x^{2} y - 2 x + 2 y^{3})

integral from 0 to pi/4 of 4tan^4(x)

\int_{0}^{\frac{π}{4}} 4 tan^{4} (x) d x

tangent of y=sin(sin(x)),(2pi,0)tangent of

y = sin (sin (x)), (2 π, 0)

Frequently Asked Questions (FAQ)

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