What is the derivative of sqrt(15t^2+9) ?

The derivative of sqrt(15t^2+9) is (15t)/(sqrt(15t^2+9))

What is the first derivative of sqrt(15t^2+9) ?

The first derivative of sqrt(15t^2+9) is (15t)/(sqrt(15t^2+9))

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derivative of

15 t^{2} + 9

\frac{15 t}{15 t ^{2} + 9}

Solution steps

\frac{d}{d t} (15 t^{2} + 9)

Apply the chain rule:

\frac{1}{2 15 t ^{2} + 9} \frac{d}{d t} (15 t^{2} + 9)

= \frac{1}{2 15 t ^{2} + 9} \frac{d}{d t} (15 t^{2} + 9)

\frac{d}{d t} (15 t^{2} + 9) = 30 t

= \frac{1}{2 15 t ^{2} + 9} \cdot 30 t

Simplify

\frac{1}{2 15 t ^{2} + 9} \cdot 30 t : \frac{15 t}{15 t ^{2} + 9}

= \frac{15 t}{15 t ^{2} + 9}

What is the derivative of sqrt(15t^2+9) ?
The derivative of sqrt(15t^2+9) is (15t)/(sqrt(15t^2+9))
What is the first derivative of sqrt(15t^2+9) ?
The first derivative of sqrt(15t^2+9) is (15t)/(sqrt(15t^2+9))