What is the derivative of sqrt(9x^2+9) ?

The derivative of sqrt(9x^2+9) is (3x)/(sqrt(x^2+1))

What is the first derivative of sqrt(9x^2+9) ?

The first derivative of sqrt(9x^2+9) is (3x)/(sqrt(x^2+1))

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

\frac{3 x}{x ^{2} + 1}

Solution steps

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

Apply the chain rule:

\frac{1}{2 9 x ^{2} + 9} \frac{d}{d x} (9 x^{2} + 9)

= \frac{1}{2 9 x ^{2} + 9} \frac{d}{d x} (9 x^{2} + 9)

\frac{d}{d x} (9 x^{2} + 9) = 18 x

= \frac{1}{2 9 x ^{2} + 9} \cdot 18 x

Simplify

\frac{1}{2 9 x ^{2} + 9} \cdot 18 x : \frac{3 x}{x ^{2} + 1}

= \frac{3 x}{x ^{2} + 1}

\int sec^{4} (5 x) d x

f (x) = 2^{x}, at x = 0

\int \frac{1}{9 + x ^{2}} d x

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

f (x) = 2 x^{2} - 4 x - 5, at x = 2

What is the derivative of sqrt(9x^2+9) ?
The derivative of sqrt(9x^2+9) is (3x)/(sqrt(x^2+1))
What is the first derivative of sqrt(9x^2+9) ?
The first derivative of sqrt(9x^2+9) is (3x)/(sqrt(x^2+1))