en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y^3+xy^2+y

Solution

\frac{d}{d x} (y^{3} + x y^{2} + y)

Solution

3 y^{2} \frac{d y}{d x} + y^{2} + 2 x y \frac{d y}{d x} + \frac{d y}{d x}

Solution steps

\frac{d}{d x} (y^{3} + x y^{2} + y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (x y^{2}) = y^{2} + 2 x y \frac{d y}{d x}

= 3 y^{2} \frac{d y}{d x} + y^{2} + 2 x y \frac{d y}{d x} + \frac{d y}{d x}

Popular Examples

derivative of ((x+1)(x^2+1))/(x-2)derivative of

\frac{( x + 1 ) ( x ^{2} + 1 )}{x - 2}

integral from-1 to 1 of (6x^5+3)

\int_{- 1}^{1} (6 x^{5} + 3) d x

derivative of y=(9x)/(e^x)derivative of

y = \frac{9 x}{e ^{x}}

f(x)=(x+1)/(x^2+1)

f (x) = \frac{x + 1}{x ^{2} + 1}

\frac{d y}{d x} - 3 y = 2

Frequently Asked Questions (FAQ)

What is the derivative of y^3+xy^2+y ?
The derivative of y^3+xy^2+y is 3y^2(dy)/(dx)+y^2+2xy(dy)/(dx)+(dy)/(dx)
What is the first derivative of y^3+xy^2+y ?
The first derivative of y^3+xy^2+y is 3y^2(dy)/(dx)+y^2+2xy(dy)/(dx)+(dy)/(dx)