What is the derivative of xsqrt(18-x^2) ?

The derivative of xsqrt(18-x^2) is (-2x^2+18)/(sqrt(18-x^2))

What is the first derivative of xsqrt(18-x^2) ?

The first derivative of xsqrt(18-x^2) is (-2x^2+18)/(sqrt(18-x^2))

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derivative of

x 18 - x^{2}

\frac{- 2 x ^{2} + 18}{18 - x ^{2}}

Solution steps

\frac{d}{d x} (x 18 - x^{2})

Apply the Product Rule:

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

f = x, g = 18 - x^{2}

= \frac{d x}{d x} 18 - x^{2} + \frac{d}{d x} (18 - x^{2}) x

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

\frac{d}{d x} (18 - x^{2}) = - \frac{x}{18 - x ^{2}}

= 1 \cdot 18 - x^{2} + (- \frac{x}{18 - x ^{2}}) x

Simplify

1 \cdot 18 - x^{2} + (- \frac{x}{18 - x ^{2}}) x : \frac{- 2 x ^{2} + 18}{18 - x ^{2}}

= \frac{- 2 x ^{2} + 18}{18 - x ^{2}}

t e^{3 t}

f (x) = \frac{1}{x - 8}, (- 1, - \frac{1}{9})

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

\int \frac{9}{25 + 16 r ^{2}} d r

\int 1 + 4 r^{2} \cdot r d r

What is the derivative of xsqrt(18-x^2) ?
The derivative of xsqrt(18-x^2) is (-2x^2+18)/(sqrt(18-x^2))
What is the first derivative of xsqrt(18-x^2) ?
The first derivative of xsqrt(18-x^2) is (-2x^2+18)/(sqrt(18-x^2))