What is the derivative of sqrt(9x^2+5) ?

The derivative of sqrt(9x^2+5) is (9x)/(sqrt(9x^2+5))

What is the first derivative of sqrt(9x^2+5) ?

The first derivative of sqrt(9x^2+5) is (9x)/(sqrt(9x^2+5))

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\frac{d}{d x} (9 x^{2} + 5)

\frac{9 x}{9 x ^{2} + 5}

Solution steps

\frac{d}{d x} (9 x^{2} + 5)

Apply the chain rule:

\frac{1}{2 9 x ^{2} + 5} \frac{d}{d x} (9 x^{2} + 5)

= \frac{1}{2 9 x ^{2} + 5} \frac{d}{d x} (9 x^{2} + 5)

\frac{d}{d x} (9 x^{2} + 5) = 18 x

= \frac{1}{2 9 x ^{2} + 5} \cdot 18 x

Simplify

\frac{1}{2 9 x ^{2} + 5} \cdot 18 x : \frac{9 x}{9 x ^{2} + 5}

= \frac{9 x}{9 x ^{2} + 5}

What is the derivative of sqrt(9x^2+5) ?
The derivative of sqrt(9x^2+5) is (9x)/(sqrt(9x^2+5))
What is the first derivative of sqrt(9x^2+5) ?
The first derivative of sqrt(9x^2+5) is (9x)/(sqrt(9x^2+5))