# Thread: Calc HW (derivatives of expo, trig and inverse functions)

1. ## Calc HW (derivatives of expo, trig and inverse functions)

I have a few problems that I am not able to figure out with my Calculus homework, I have solved most of them but am stuck on these. Working full time and going to school full time does not give me much time to find an actual 'person-to-person' tutor and only three hours a week in class does not seem to be enough time for me to grasp the concepts of some of these problems at times. Although I am a new user and this is my first post, I will be going through college for the next four to five years, so I plan to stay with this forum throughout my college career to get a decent study in. Going home and reviewing notes or doing problems out of the book never seemed to help me much, usually when I have someone explain how to do it or show me little tricks or shortcuts, I learn a little bit better.

1) Let S = F(T) = 160T - 16T^2 Represent position of a thrown ball as a function of time.
A)When does the ball reach a maximum height?
B)When does the ball hit the ground?

2) Find the derivative of Y = TanA/(1-TanA)

For this problem I got:
Sec^2(A)/(1-TanA)^2

I just wanted to make sure this was right, if you want to see the work I did on it, let me know.

3) Find the derivative of Y = e^(Sin2x)

4) Find the derivative of Y = Tan^2 (2A)

5) Find th ederivative of F(X) = xe^(-2x)

6) Find DY/DX at the point (-2,1) for Y^2 - 2X - 4Y - 4 = 0

7) Let F(X) = 1 - 8X^3 Find the derivative of the inverse function at the point (-7, 1)

8) Find the second derivative of Y = 2Sin^2(X) + 2Cos^2(X)

Even help with just one of these problems would be apperciated. I have tried to do all of them but just get confused and the page looks messy when I'm done with numbers and letters written everywhere. Thank you in advanced even if you can shed some light onto some of these problems for me.

2. 1) $\displaystyle S(t) = 160t-16t^2$

A- Derive the equation (simple) and find the critical numbers. The derivative of position is velocity, so if you think about it when you throw a ball in the air, the top of the arc is a point where the ball has no velocity (just after it stops going up but before it starts falling), so it's simple. After you have the derivative find where it's equal to 0 (critical numbers), and the largest S for those t is your answer.
B- Set S(t) = 0 and solve. 0 isn't the answer.

3) Find the derivative of [tex]F(x) = e^{sin2x}
Use the Chain Rule. $\displaystyle u(x) = e^x$; $\displaystyle v(x) = sin2x$. You'll have to use the Chain Rule again on v(x) to find the derivative.

8) Where are you stuck? You should be able to write the function as $\displaystyle F(x) = 2((sinx)(sinx)) + 2((cosx)(cosx))$ and just solve as the product rule.

3. Originally Posted by Open that Hampster!
1) $\displaystyle S(t) = 160t-16t^2$

A- Derive the equation (simple) and find the critical numbers. The derivative of position is velocity, so if you think about it when you throw a ball in the air, the top of the arc is a point where the ball has no velocity (just after it stops going up but before it starts falling), so it's simple. After you have the derivative find where it's equal to 0 (critical numbers), and the largest S for those t is your answer.
B- Set S(t) = 0 and solve. 0 isn't the answer.

3) Find the derivative of [tex]F(x) = e^{sin2x}
Use the Chain Rule. $\displaystyle u(x) = e^x$; $\displaystyle v(x) = sin2x$. You'll have to use the Chain Rule again on v(x) to find the derivative.

8) Where are you stuck? You should be able to write the function as $\displaystyle F(x) = 2((sinx)(sinx)) + 2((cosx)(cosx))$ and just solve as the product rule.
For:
1A - I got 5 seconds
1B - I got 16 seconds

3 - I got Cos2xe^{sin2x}

8 - I got 8CosX-8SinX

You don't have to tell me the correct answers, just if they are right or wrong would be helpful. If they are wrong I will try again. Anyone else with any help on the other problems? Please and thank you.

4. Bump. No one?