What is the derivative of 2xy^2+4 ?

The derivative of 2xy^2+4 is 2(2xy(dy)/(dx)+y^2)

What is the first derivative of 2xy^2+4 ?

The first derivative of 2xy^2+4 is 2(2xy(dy)/(dx)+y^2)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x y^{2}) + \frac{d}{d x} (4)

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

\frac{d}{d x} (4) = 0

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

Simplify

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

What is the derivative of 2xy^2+4 ?
The derivative of 2xy^2+4 is 2(2xy(dy)/(dx)+y^2)
What is the first derivative of 2xy^2+4 ?
The first derivative of 2xy^2+4 is 2(2xy(dy)/(dx)+y^2)