What is (\partial)/(\partial x)(2pixy+pix^2) ?

The answer to (\partial)/(\partial x)(2pixy+pix^2) is 2piy+2pix

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(\partial)/(\partial x)(2pixy+pix^2)

\frac{\partial}{\partial x} (2 π x y + π x^{2})

2 π y + 2 π x

Solution steps

\frac{\partial}{\partial x} (2 π x y + π x^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 π x y) = 2 π y

\frac{\partial}{\partial x} (π x^{2}) = 2 π x

= 2 π y + 2 π x

\frac{\partial}{\partial x} (e^{- 3 x})

cos (y) + (1 + e^{- x}) sin (y) \frac{d y}{d x} = 0

\int \frac{1}{5 x + 4} d x

x \to 0 lim (\frac{cos ( 4 x ) - cos ( 2 x )}{x ^{2}})

\frac{d}{d x} (\frac{1 - x ^{2}}{( x ^{2} + 1 ) ^{2}})

What is (\partial)/(\partial x)(2pixy+pix^2) ?
The answer to (\partial)/(\partial x)(2pixy+pix^2) is 2piy+2pix