What is the derivative of y=3+sqrt(9-(x-3)^2) ?

The derivative of y=3+sqrt(9-(x-3)^2) is (-x+3)/(sqrt(-x^2+6x))

What is the first derivative of y=3+sqrt(9-(x-3)^2) ?

The first derivative of y=3+sqrt(9-(x-3)^2) is (-x+3)/(sqrt(-x^2+6x))

derivative of

y = 3 + 9 - (x - 3)^{2}

\frac{- x + 3}{- x ^{2} + 6 x}

Solution steps

\frac{d}{d x} (3 + 9 - (x - 3)^{2})

Simplify

3 + 9 - (x - 3)^{2} : 3 + - x^{2} + 6 x

= \frac{d}{d x} (3 + - x^{2} + 6 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3) + \frac{d}{d x} (- x^{2} + 6 x)

\frac{d}{d x} (3) = 0

\frac{d}{d x} (- x^{2} + 6 x) = \frac{- x + 3}{- x ^{2} + 6 x}

= 0 + \frac{- x + 3}{- x ^{2} + 6 x}

Simplify

= \frac{- x + 3}{- x ^{2} + 6 x}

d er i v a t i v e f (x) = \frac{4}{5 x + 1}

\int \frac{2 x}{x ^{2} + 6} d x

5 y^{^{'}} = y^{2}

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

d er i v a t i v e ln (x y)

What is the derivative of y=3+sqrt(9-(x-3)^2) ?
The derivative of y=3+sqrt(9-(x-3)^2) is (-x+3)/(sqrt(-x^2+6x))
What is the first derivative of y=3+sqrt(9-(x-3)^2) ?
The first derivative of y=3+sqrt(9-(x-3)^2) is (-x+3)/(sqrt(-x^2+6x))