I was absent for the first time in my math class due to an emergency and now I'm falling behind everyone else in the class. I really need some help differentiating these functions. Please help me!
Let's take these one at a time. First, it would be helpful to know what your thoughts are on how to differentiate the function in part a). Do you know the power rule? Do you know how to differentiate trigonometric functions?
The derivatives of the secant and cosine are SecXTanX and -Sinx, correct? I'm still very confused about approaching this problem. This might seem easy to you guys because you are all math geniuses here but I have a hard time with math in general.
Hey, we were all students once, we all had to learn, and you are doing fine. You have correctly given the power rule, and the rules for the two trig. functions involved, so now you just need to put it all together, term by term. What is your result?
You need to work the problems step by step.
Let's start with a.
We can take the derivative of each individual portion.
f'(x) = (2x^4)' + (5sec(x))' - (3cos(x))' - (x^-4)'
Power rule: (2x^4)' = 8x^3
Secant Function: (5sec(x))' = 5sec(x)tan(x)
Cosine Function: (3cos(x))' = -3sin(x)
Power rule: (x^-4)' = -4x^-5
Now, sub back into the formula.
f'(x) = 6x^3 + 5sec(x)tan(x) + 3sin(x) + 4x^-5
If you are having trouble with the individual portions, that is mostly a memorization task. Just study the properties of derivatives.
Don't feel dumb. Really, everyone had to learn this at some point. It wasn't easy at first.
Also, if you want a reference page try this one calculus. Mathwords: Derivative Rules
It has all of the basic rules on it, it is very helpful.