What is the derivative of 5x^2sqrt(25-x^2) ?

The derivative of 5x^2sqrt(25-x^2) is (5(-3x^3+50x))/(sqrt(25-x^2))

What is the first derivative of 5x^2sqrt(25-x^2) ?

The first derivative of 5x^2sqrt(25-x^2) is (5(-3x^3+50x))/(sqrt(25-x^2))

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derivative of

5 x^{2} 25 - x^{2}

\frac{5 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (5 x^{2} 25 - x^{2})

Take the constant out:

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

= 5 \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}

= 5 (\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}}

= 5 (2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2})

Simplify

5 (2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2}) : \frac{5 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

= \frac{5 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

What is the derivative of 5x^2sqrt(25-x^2) ?
The derivative of 5x^2sqrt(25-x^2) is (5(-3x^3+50x))/(sqrt(25-x^2))
What is the first derivative of 5x^2sqrt(25-x^2) ?
The first derivative of 5x^2sqrt(25-x^2) is (5(-3x^3+50x))/(sqrt(25-x^2))