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^3

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = y^{3}

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

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

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

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

Popular Examples

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

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

derivative of 2^{5x}

\frac{d}{d x} (2^{5 x})

tangent of f(x)=-7-x^2,\at x=9 tangent of

f (x) = - 7 - x^{2}, at x = 9

derivative of (xcos(x-2pi)/(x-2pi))

\frac{d}{d x} (\frac{x cos ( x ) - 2 π}{x - 2 π})

derivative of (1-cos(x)/(1-sin(x)))

\frac{d}{d x} (\frac{1 - cos ( x )}{1 - sin ( x )})

Frequently Asked Questions (FAQ)

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