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Popular >

derivative of 2x^2y^3

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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}

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

Popular Examples

integral of x/2 sqrt(4+x^2)

\int \frac{x}{2} 4 + x^{2} d x

(\partial)/(\partial x)(4x^3y^2)

\frac{\partial}{\partial x} (4 x^{3} y^{2})

integral of (1-2x^2)

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

integral of (6x^2-7x+3)

\int (6 x^{2} - 7 x + 3) d x

integral of (tan(x/6))^5

\int (tan (\frac{x}{6}))^{5} d x

Frequently Asked Questions (FAQ)

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