en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of cos(x)x^3

Solution

derivative of

cos (x) x^{3}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral from-pi to pi of cos(nx)cos(mx)

\int_{- π}^{π} cos (n x) cos (m x) d x

y^{''}-12y^'+36y=te^{6t}

y^{^{''}} - 12 y^{^{'}} + 36 y = t e^{6 t}

integral of sin((npix)/4)

\int sin (\frac{nπ x}{4}) d x

derivative of (2+sin(x)/(2x+cos(x)))

\frac{d}{d x} (\frac{2 + sin ( x )}{2 x + cos ( x )})

area y=|x|,y=x^2-1,x=-1,x=1 area

y = ∣ x ∣, y = x^{2} - 1, x = - 1, x = 1

Frequently Asked Questions (FAQ)

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