What is the derivative of sqrt(11t^2+9) ?

The derivative of sqrt(11t^2+9) is (11t)/(sqrt(11t^2+9))

What is the first derivative of sqrt(11t^2+9) ?

The first derivative of sqrt(11t^2+9) is (11t)/(sqrt(11t^2+9))

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derivative of

11 t^{2} + 9

\frac{11 t}{11 t ^{2} + 9}

Solution steps

\frac{d}{d t} (11 t^{2} + 9)

Apply the chain rule:

\frac{1}{2 11 t ^{2} + 9} \frac{d}{d t} (11 t^{2} + 9)

= \frac{1}{2 11 t ^{2} + 9} \frac{d}{d t} (11 t^{2} + 9)

\frac{d}{d t} (11 t^{2} + 9) = 22 t

= \frac{1}{2 11 t ^{2} + 9} \cdot 22 t

Simplify

\frac{1}{2 11 t ^{2} + 9} \cdot 22 t : \frac{11 t}{11 t ^{2} + 9}

= \frac{11 t}{11 t ^{2} + 9}

What is the derivative of sqrt(11t^2+9) ?
The derivative of sqrt(11t^2+9) is (11t)/(sqrt(11t^2+9))
What is the first derivative of sqrt(11t^2+9) ?
The first derivative of sqrt(11t^2+9) is (11t)/(sqrt(11t^2+9))