What is the derivative of (sqrt(9-x^2))(1/3)pix^2 ?

The derivative of (sqrt(9-x^2))(1/3)pix^2 is (pix(-x^2+6))/(sqrt(9-x^2))

What is the first derivative of (sqrt(9-x^2))(1/3)pix^2 ?

The first derivative of (sqrt(9-x^2))(1/3)pix^2 is (pix(-x^2+6))/(sqrt(9-x^2))

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derivative of

(9 - x^{2}) (\frac{1}{3}) π x^{2}

\frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

Solution steps

\frac{d}{d x} (9 - x^{2} \frac{1}{3} π x^{2})

Take the constant out:

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

= \frac{1}{3} π \frac{d}{d x} (9 - x^{2} x^{2})

Apply the Product Rule:

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

f = 9 - x^{2}, g = x^{2}

= \frac{1}{3} π (\frac{d}{d x} (9 - x^{2}) x^{2} + \frac{d}{d x} (x^{2}) 9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

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

= \frac{1}{3} π ((- \frac{x}{9 - x ^{2}}) x^{2} + 2 x 9 - x^{2})

Simplify

\frac{1}{3} π ((- \frac{x}{9 - x ^{2}}) x^{2} + 2 x 9 - x^{2}) : \frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

= \frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

What is the derivative of (sqrt(9-x^2))(1/3)pix^2 ?
The derivative of (sqrt(9-x^2))(1/3)pix^2 is (pix(-x^2+6))/(sqrt(9-x^2))
What is the first derivative of (sqrt(9-x^2))(1/3)pix^2 ?
The first derivative of (sqrt(9-x^2))(1/3)pix^2 is (pix(-x^2+6))/(sqrt(9-x^2))