What is the derivative of sqrt(4x^2+9) ?

The derivative of sqrt(4x^2+9) is (4x)/(sqrt(4x^2+9))

What is the first derivative of sqrt(4x^2+9) ?

The first derivative of sqrt(4x^2+9) is (4x)/(sqrt(4x^2+9))

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\frac{d}{d x} (4 x^{2} + 9)

\frac{4 x}{4 x ^{2} + 9}

Solution steps

\frac{d}{d x} (4 x^{2} + 9)

Apply the chain rule:

\frac{1}{2 4 x ^{2} + 9} \frac{d}{d x} (4 x^{2} + 9)

= \frac{1}{2 4 x ^{2} + 9} \frac{d}{d x} (4 x^{2} + 9)

\frac{d}{d x} (4 x^{2} + 9) = 8 x

= \frac{1}{2 4 x ^{2} + 9} \cdot 8 x

Simplify

\frac{1}{2 4 x ^{2} + 9} \cdot 8 x : \frac{4 x}{4 x ^{2} + 9}

= \frac{4 x}{4 x ^{2} + 9}

What is the derivative of sqrt(4x^2+9) ?
The derivative of sqrt(4x^2+9) is (4x)/(sqrt(4x^2+9))
What is the first derivative of sqrt(4x^2+9) ?
The first derivative of sqrt(4x^2+9) is (4x)/(sqrt(4x^2+9))