What is the derivative of 5x^2y ?

The derivative of 5x^2y is 10xy

What is the first derivative of 5x^2y ?

The first derivative of 5x^2y is 10xy

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derivative of

5 x^{2} y

10 x y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 y \cdot 2 x^{2 - 1}

Simplify

= 10 x y

x \to 0 lim (\frac{7 x ^{3} - x ^{2}}{x})

(x^{2} + y^{2}) d x - (2 \cdot x \cdot y) d y = 0

x \to 1 - lim (f (x))

\int \frac{x ^{3} + 5}{x ^{2} + 3 x + 2} d x

\int - 7 cos^{2} (x) tan^{3} (x) d x