What is the derivative of pix^2y ?

The derivative of pix^2y is pi(2xy+(dy)/(dx)x^2)

What is the first derivative of pix^2y ?

The first derivative of pix^2y is pi(2xy+(dy)/(dx)x^2)

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\frac{d}{d x} (π x^{2} y)

π (2 x y + \frac{d y}{d x} x^{2})

Solution steps

\frac{d}{d x} (π x^{2} y)

Take the constant out:

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

= π \frac{d}{d x} (x^{2} y)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y

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

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

= π (2 x y + \frac{d y}{d x} x^{2})

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6 x^{4} ln (x)

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