What is the derivative of 1/3 pix^2y ?

The derivative of 1/3 pix^2y is pi/3 (2xy+x^2(dy)/(dx))

What is the first derivative of 1/3 pix^2y ?

The first derivative of 1/3 pix^2y is pi/3 (2xy+x^2(dy)/(dx))

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\frac{d}{d x} (\frac{1}{3} π x^{2} y)

\frac{π}{3} (2 x y + x^{2} \frac{d y}{d x})

Solution steps

\frac{d}{d x} (\frac{1}{3} π x^{2} y)

Take the constant out:

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

= \frac{1}{3} 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

= \frac{1}{3} π (\frac{d}{d x} (x^{2}) y + \frac{d y}{d x} x^{2})

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

= \frac{1}{3} π (2 x y + \frac{d y}{d x} x^{2})

Simplify

\frac{1}{3} π (2 x y + \frac{d y}{d x} x^{2}) : \frac{π}{3} (2 x y + x^{2} \frac{d y}{d x})

= \frac{π}{3} (2 x y + x^{2} \frac{d y}{d x})

What is the derivative of 1/3 pix^2y ?
The derivative of 1/3 pix^2y is pi/3 (2xy+x^2(dy)/(dx))
What is the first derivative of 1/3 pix^2y ?
The first derivative of 1/3 pix^2y is pi/3 (2xy+x^2(dy)/(dx))