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Popular Calculus >

derivative of y=x^2sqrt(16-x^2)

Solution

derivative of

y = x^{2} 16 - x^{2}

Solution

\frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} 16 - x^{2})

Apply the Product Rule:

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

f = x^{2}, g = 16 - x^{2}

= \frac{d}{d x} (x^{2}) 16 - x^{2} + \frac{d}{d x} (16 - x^{2}) x^{2}

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

\frac{d}{d x} (16 - x^{2}) = - \frac{x}{16 - x ^{2}}

= 2 x 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x^{2}

Simplify

2 x 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

= \frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^2sqrt(16-x^2) ?
The derivative of y=x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))
What is the first derivative of y=x^2sqrt(16-x^2) ?
The first derivative of y=x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))