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Popular >

derivative of y^2x+5xy^3+10y^2+8xy

Solution

derivative of

y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y

Solution

2 x y + 15 x y^{2} + 20 y + 8 x

Solution steps

\frac{d}{d y} (y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d y} (y^{2} x) + \frac{d}{d y} (5 x y^{3}) + \frac{d}{d y} (10 y^{2}) + \frac{d}{d y} (8 x y)

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

\frac{d}{d y} (5 x y^{3}) = 15 x y^{2}

\frac{d}{d y} (10 y^{2}) = 20 y

\frac{d}{d y} (8 x y) = 8 x

= 2 x y + 15 x y^{2} + 20 y + 8 x

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Frequently Asked Questions (FAQ)

What is the derivative of y^2x+5xy^3+10y^2+8xy ?
The derivative of y^2x+5xy^3+10y^2+8xy is 2xy+15xy^2+20y+8x
What is the first derivative of y^2x+5xy^3+10y^2+8xy ?
The first derivative of y^2x+5xy^3+10y^2+8xy is 2xy+15xy^2+20y+8x