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Popular >

derivative of 2xy^3

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = y^{3}

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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