en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 3x^2y^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = y^{2}

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

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

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

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

Popular Examples

derivative of x(1-x^2^{1/2})

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

sum from n=0 to infinity of i(-1)^n

n = 0 \sum \infty i (- 1)^{n}

(x+sqrt(x))(dy)/(dx)=y+sqrt(y)

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

derivative of 4arccos(sqrt(1-x^2))

\frac{d}{d x} (4 arccos (1 - x^{2}))

(\partial)/(\partial y)(-2y^2)

\frac{\partial}{\partial y} (- 2 y^{2})

Frequently Asked Questions (FAQ)

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