What is the derivative of 6sqrt(8x^2+9) ?

The derivative of 6sqrt(8x^2+9) is (48x)/(sqrt(8x^2+9))

What is the first derivative of 6sqrt(8x^2+9) ?

The first derivative of 6sqrt(8x^2+9) is (48x)/(sqrt(8x^2+9))

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derivative of

6 8 x^{2} + 9

\frac{48 x}{8 x ^{2} + 9}

Solution steps

\frac{d}{d x} (6 8 x^{2} + 9)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (8 x^{2} + 9)

Apply the chain rule:

\frac{1}{2 8 x ^{2} + 9} \frac{d}{d x} (8 x^{2} + 9)

= \frac{1}{2 8 x ^{2} + 9} \frac{d}{d x} (8 x^{2} + 9)

\frac{d}{d x} (8 x^{2} + 9) = 16 x

= 6 \cdot \frac{1}{2 8 x ^{2} + 9} \cdot 16 x

Simplify

6 \cdot \frac{1}{2 8 x ^{2} + 9} \cdot 16 x : \frac{48 x}{8 x ^{2} + 9}

= \frac{48 x}{8 x ^{2} + 9}

What is the derivative of 6sqrt(8x^2+9) ?
The derivative of 6sqrt(8x^2+9) is (48x)/(sqrt(8x^2+9))
What is the first derivative of 6sqrt(8x^2+9) ?
The first derivative of 6sqrt(8x^2+9) is (48x)/(sqrt(8x^2+9))