What is the derivative of x^2y+3x*y^3+x ?

The derivative of x^2y+3x*y^3+x is 2xy+(dy)/(dx)x^2+3(y^3+3xy^2(dy)/(dx))+1

What is the first derivative of x^2y+3x*y^3+x ?

The first derivative of x^2y+3x*y^3+x is 2xy+(dy)/(dx)x^2+3(y^3+3xy^2(dy)/(dx))+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

2 x y + \frac{d y}{d x} x^{2} + 3 (y^{3} + 3 x y^{2} \frac{d y}{d x}) + 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d x}{d x} = 1

= 2 x y + \frac{d y}{d x} x^{2} + 3 (y^{3} + 3 x y^{2} \frac{d y}{d x}) + 1

\int cot (6 x) d x

\frac{\partial}{\partial z} (x^{3})

x^{2} sin^{2} (5 x)

y = 5 e^{x}

\int \frac{x}{x - 1} d x

What is the derivative of x^2y+3x*y^3+x ?
The derivative of x^2y+3x*y^3+x is 2xy+(dy)/(dx)x^2+3(y^3+3xy^2(dy)/(dx))+1
What is the first derivative of x^2y+3x*y^3+x ?
The first derivative of x^2y+3x*y^3+x is 2xy+(dy)/(dx)x^2+3(y^3+3xy^2(dy)/(dx))+1