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Popular >

derivative of 5xy^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = y^{2}

= 5 (\frac{d x}{d x} y^{2} + \frac{d}{d x} (y^{2}) x)

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

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

= 5 (1 \cdot y^{2} + 2 y \frac{d y}{d x} x)

Simplify

= 5 (y^{2} + 2 x y \frac{d y}{d x})

Popular Examples

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\frac{d x}{d t} = \frac{( e ^{t} - e ^{- t} )}{x + 3}

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\int \frac{1}{x ^{2} - 6 x + 5} d x

(\partial)/(\partial x)(2(x+v(x,t)t))

\frac{\partial}{\partial x} (2 (x + v (x, t) t))

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Frequently Asked Questions (FAQ)

What is the derivative of 5xy^2 ?
The derivative of 5xy^2 is 5(y^2+2xy(dy)/(dx))
What is the first derivative of 5xy^2 ?
The first derivative of 5xy^2 is 5(y^2+2xy(dy)/(dx))