What is the derivative of xsqrt(3600-x^2) ?

The derivative of xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))

What is the first derivative of xsqrt(3600-x^2) ?

The first derivative of xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))

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derivative of

x 3600 - x^{2}

\frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

Solution steps

\frac{d}{d x} (x 3600 - x^{2})

Apply the Product Rule:

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

f = x, g = 3600 - x^{2}

= \frac{d x}{d x} 3600 - x^{2} + \frac{d}{d x} (3600 - x^{2}) x

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

\frac{d}{d x} (3600 - x^{2}) = - \frac{x}{3600 - x ^{2}}

= 1 \cdot 3600 - x^{2} + (- \frac{x}{3600 - x ^{2}}) x

Simplify

1 \cdot 3600 - x^{2} + (- \frac{x}{3600 - x ^{2}}) x : \frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

= \frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

3 e^{- 2 t} + e^{- t}

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{2})

\int \frac{1}{x 1 + x} d x

\int e^{3 x + 9} d x

\frac{d}{d x} (e^{- 2 x^{3} + 2})

What is the derivative of xsqrt(3600-x^2) ?
The derivative of xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))
What is the first derivative of xsqrt(3600-x^2) ?
The first derivative of xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))