Find the tangent line at point (3,2)

Now that we know dy/dx, solve for the slope using the given values for (x and y)

Now use the Tangent Line formula

**Next Problem**

Now to find the tangent line for this problem, with the coordinates (2,0)

A brief aside

**Prove derivative of ln(x) using Implicit Differentiation**

- The Problem
- Write in full form, including y
- Use log properties to arrange into
*x =*form - Take the derivative with respect to the change in x from both sides
- The derivative of
*“e to the y”*remains*“e to the y”,*the derivative of x is one. - Rearrange to solve for the derivative
*dy/dx*. - Substitute for
*y.* *“e to the ln of anything” is equal to the anything, in this case anything is x.*

**Find the derivative of arcsin x.**

- The Problem
- Rearrange the problem using Trig
- Take the derivative from both sides
- x is equal to 1
- Solve for dy/dx
- Substitute for y in the solution.
- The professor kept going and somehow (using Trig?) managed to bring the answer to this.

This is what he did:

Not quite sure how cos y equaled x

**Increasing and decreasing functions**

For sin to be invertable, you need to restrict the domain to -pi/2 to pi/2

To see how a function looks, determine the invervals above and below zero. To do this solve for x.

You can look at the derivaties to decide in a function is concave up or concave down.

Second derivative is negative, concave down. Second derivative is positive, concave up

READ problem 2.7 #43 from the textbook.