en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=x^3cos(x)

Solution

derivative of

y = 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 2 of ((x+2)/(x-4))

\int_{0}^{2} (\frac{x + 2}{x - 4}) d x

integral of e^{7θ}sin(8θ)

\int e^{7 θ} sin (8 θ) d θ

integral of 4e^{-0.1x}

\int 4 e^{- 0.1 x} d x

area 3sin(2x),-2pi,pi area

3 sin (2 x), - 2 π, π

limit as x approaches 0 of ((3arccos(1/2+x)-3arccos(1/2)))/x

x \to 0 lim (\frac{( 3 arccos ( \frac{1}{2} + x ) - 3 arccos ( \frac{1}{2} ) )}{x})

Frequently Asked Questions (FAQ)

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