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Popular >

derivative of 2x^3y^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(cos(x))

\frac{\partial}{\partial x} (cos (x))

derivative of y=x(x-2)^3 derivative of

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x \to \infty lim (\frac{3 x}{5})

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

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

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\int_{- 1}^{1} e^{x} - (x^{2} - 1) d x

Frequently Asked Questions (FAQ)

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