What is the derivative of xsqrt(400-x^2) ?

The derivative of xsqrt(400-x^2) is (-2x^2+400)/(sqrt(400-x^2))

What is the first derivative of xsqrt(400-x^2) ?

The first derivative of xsqrt(400-x^2) is (-2x^2+400)/(sqrt(400-x^2))

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\frac{d}{d x} (x 400 - x^{2})

\frac{- 2 x ^{2} + 400}{400 - x ^{2}}

Solution steps

\frac{d}{d x} (x 400 - x^{2})

Apply the Product Rule:

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

f = x, g = 400 - x^{2}

= \frac{d x}{d x} 400 - x^{2} + \frac{d}{d x} (400 - x^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (400 - x^{2}) = - \frac{x}{400 - x ^{2}}

= 1 \cdot 400 - x^{2} + (- \frac{x}{400 - x ^{2}}) x

Simplify

1 \cdot 400 - x^{2} + (- \frac{x}{400 - x ^{2}}) x : \frac{- 2 x ^{2} + 400}{400 - x ^{2}}

= \frac{- 2 x ^{2} + 400}{400 - x ^{2}}

5 y^{^{'}} + 15 y = 375, y (0) = 0

e^{x}, 1

n = 0 \sum \infty - \frac{n}{2 ^{n}}

x^{4} - 2 x^{2}, 2 x^{2}

x \to \infty lim (x^{n})

What is the derivative of xsqrt(400-x^2) ?
The derivative of xsqrt(400-x^2) is (-2x^2+400)/(sqrt(400-x^2))
What is the first derivative of xsqrt(400-x^2) ?
The first derivative of xsqrt(400-x^2) is (-2x^2+400)/(sqrt(400-x^2))