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Popular Calculus >

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

integral of 1/(x^2-6x+5)

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

derivative of 7(x^2+3x)^6(2x+3)

d er i v a t i v e 7 (x^{2} + 3 x)^{6} (2 x + 3)

integral of e^{x/(60)}

\int e^{\frac{x}{60}} d x

derivative of x^4a^5+y^3a+z^6

d er i v a t i v e x^{4} a^{5} + y^{3} a + z^{6}

y^{''}+y=xcos^3(x)

y^{^{''}} + y = x cos^{3} (x)

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))