What is the derivative of y=x^2sqrt(25-x^2) ?

The derivative of y=x^2sqrt(25-x^2) is (-3x^3+50x)/(sqrt(25-x^2))

What is the first derivative of y=x^2sqrt(25-x^2) ?

The first derivative of y=x^2sqrt(25-x^2) is (-3x^3+50x)/(sqrt(25-x^2))

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derivative of

y = x^{2} 25 - x^{2}

\frac{- 3 x ^{3} + 50 x}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} 25 - x^{2})

Apply the Product Rule:

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

f = x^{2}, g = 25 - x^{2}

= \frac{d}{d x} (x^{2}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{2}

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2}

Simplify

2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 50 x}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 50 x}{25 - x ^{2}}

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What is the derivative of y=x^2sqrt(25-x^2) ?
The derivative of y=x^2sqrt(25-x^2) is (-3x^3+50x)/(sqrt(25-x^2))
What is the first derivative of y=x^2sqrt(25-x^2) ?
The first derivative of y=x^2sqrt(25-x^2) is (-3x^3+50x)/(sqrt(25-x^2))