Do you remember the Power Rule, the Product Rule, and the Chain Rule? Here are two additional formulas that will help:
For the final problem, we may differentiate both sides and express in terms of and .
I've gotten some excellent help on these forums today. A HUGE thank you to everyone who assisted.
3 more questions giving me issues. If you could at least help get me started I would appreciate that...no need to do all my homework for me lol
Find the derivative of the following functions-
f(t)=tan^-1(e^4t-2)tan(e^t+1)
g(z)=ln(z^2)-5ze^(2z-1)
Given e^(x^2)+y^6=3xtan(y), find y'
I'm not really sure where to start on these
I can't remember the derivative of a inverse tangent, but just look it up and use the chain rule. For example, to find g'(z), use the chain rule:
You should know that the derivative of a function is just
So to differentiate g(z):
Do you see how I applied the power rule and the chain rule?
Calculus isn't easy. It took the genius of Isaac Newton to develop, so don't be discouraged.
Do you understand why you have to apply the product rule to ?
Remember that you defined x and y as functions of t when you wrote:
and
This means that is a function of a function. The same is true with . In order to differentiate I have to apply the chain rule.
If we consider the function:
we have the derivative:
You don't want leave it in this form since , you should substitute this for the
Can you tell what the derivative with respect to t of is?