# (Q14.) So, you think you can take the derivative? | Summary and Q&A

251 views
April 13, 2014
by
blackpenredpen
(Q14.) So, you think you can take the derivative?

## TL;DR

The second derivative of ln(secant x + tangent x) is secant x times tangent x.

## Install to Summarize YouTube Videos and Get Transcripts

### Q: What is the first derivative of ln(secant x + tangent x)?

The first derivative is secant x.

Explanation: The derivative of ln(secant x + tangent x) is equal to 1 divided by (secant x + tangent x), multiplied by the derivative of (secant x + tangent x), which simplifies to secant x.

### Q: How do you find the second derivative of ln(secant x + tangent x)?

To find the second derivative, differentiate the first derivative with respect to x.

Explanation: The derivative of secant x is secant x times tangent x. Therefore, the second derivative of ln(secant x + tangent x) is secant x times tangent x.

### Q: Can the expression ln(secant x + tangent x) be simplified?

Yes, the expression can be simplified by factoring out the common term secant x from the numerator.

Explanation: By factoring out secant x, the expression becomes secant x times (tangent x + secant x) divided by (secant x + tangent x). The numerator simplifies to secant x times tangent x plus secant squared x. However, in the denominator, the order of addition doesn't matter, so tangent x + secant x is the same as secant x + tangent x. These two terms cancel out, leaving the simplified expression as secant x.

### Q: What is the final answer for the second derivative of ln(secant x + tangent x)?

The answer is secant x times tangent x.

Explanation: After simplifying the expression and differentiating the first derivative of ln(secant x + tangent x), we get secant x times tangent x as the second derivative.

## Summary & Key Takeaways

• The first derivative of ln(secant x + tangent x) is secant x.

• To find the second derivative, you need to differentiate the first derivative with respect to x.

• The derivative of secant x is secant x times tangent x.