What is the derivative of sqrt(9x-45) ?

The derivative of sqrt(9x-45) is 3/(2sqrt(x-5))

What is the first derivative of sqrt(9x-45) ?

The first derivative of sqrt(9x-45) is 3/(2sqrt(x-5))

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\frac{d}{d x} (9 x - 45)

\frac{3}{2 x - 5}

Solution steps

\frac{d}{d x} (9 x - 45)

Apply the chain rule:

\frac{1}{2 9 x - 45} \frac{d}{d x} (9 x - 45)

= \frac{1}{2 9 x - 45} \frac{d}{d x} (9 x - 45)

\frac{d}{d x} (9 x - 45) = 9

= \frac{1}{2 9 x - 45} \cdot 9

Simplify

\frac{1}{2 9 x - 45} \cdot 9 : \frac{3}{2 x - 5}

= \frac{3}{2 x - 5}

d er i v a t i v e f (x) = 4 x^{- 3} + x^{2} + 14

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

x \to 0 lim (x^{4 s i n (x)})

d er i v a t i v e f (x) = \frac{x}{x + 8}

\int \frac{x - 3}{3 x ^{5}} d x

What is the derivative of sqrt(9x-45) ?
The derivative of sqrt(9x-45) is 3/(2sqrt(x-5))
What is the first derivative of sqrt(9x-45) ?
The first derivative of sqrt(9x-45) is 3/(2sqrt(x-5))