Differentiate each function?

[stinajeana]

f(x)= (e^x)+(pi^x)+(e^pi)+(x^e)
g(x)= (e^sinx)+(csc(e^x))

I'm not quite sure where to begin... help?
Also, I don't want the answer. Just want to know where to begin

 

[stapel]

f(x)= (e^x)+(pi^x)+(e^pi)+(x^e)
g(x)= (e^sinx)+(csc(e^x))

I'm not quite sure where to begin...

For f(x), you have a sum of four terms. In the first and second terms, you have numbers to a variable power. Apply the appropriate rule. (Review the list of rules they gave you, if you're not sure.) The third term is just a number. The fourth term is a variable to a numerical power; apply the appropriate rule.

For g(x), you'll need to apply the Chain Rule to each of the two terms. For the first term, you'll start by differentiating the exponential, and then you'll differentiate what is in the exponent. For the second, you'll start by differentiating the trig function; then you'll differentiate the argument of that function.

If you get stuck, please reply showing how far you have gotten for each of the terms. Thank you.

 

[HallsofIvy]

For any positive number, a, \(\displaystyle a^x=e^{ln(a^x)}= e^{x ln(a)}\). I presume you know that the derivative of \(\displaystyle e^{bx}\) is \(\displaystyle be^{bx}\) so the derivative of \(\displaystyle a^x\) is \(\displaystyle ln(a)e^{x ln(a)}= ln(a) a^x\).

 

[whiteti]

hi, I'm working on the same problems.

for g(x)= e^sinx + csc(e^x) i got
g'(x)= e^sinx * cosx - csc e^x * cot e^x
Correct?

For f(x) i dont know what rule would apply here

 

[srmichael]

hi, I'm working on the same problems.

for g(x)= e^sinx + csc(e^x) i got
g'(x)= e^sinx * cosx - csc e^x * cot e^x ====> ALMOST
Correct?

For f(x) i dont know what rule would apply here

Don't forget to apply chain rule and multiply the derivative of the csc(e^x) by the derivative of the angle, which is e^x.

Thus, g'(x) = (e^sinx)(cosx) - [csc(e^x)cot(e^x)](e^x)

 

[whiteti]

so for f(x)

Ive got f'(x) = e^x+0+ ___ +____

not sure how to differentiatie e^pi or x^e... or if I should be using a rule here

 

[mmm4444bot]

not sure how to differentiatie e^pi

What class are you currently taking?

 

[whiteti]

Calculus 1 in university. I GET IT, I'm an idiot because I have not studied precalculus.

so how do i differentiate e^pi and x^e?

should I be doing each term individually?

 

[stinajeana]

For f(x), you have a sum of four terms. In the first and second terms, you have numbers to a variable power. Apply the appropriate rule. (Review the list of rules they gave you, if you're not sure.) The third term is just a number. The fourth term is a variable to a numerical power; apply the appropriate rule.

For g(x), you'll need to apply the Chain Rule to each of the two terms. For the first term, you'll start by differentiating the exponential, and then you'll differentiate what is in the exponent. For the second, you'll start by differentiating the trig function; then you'll differentiate the argument of that function.

If you get stuck, please reply showing how far you have gotten for each of the terms. Thank you.

f'(x)=(e^x)+(lnpi)(pi^x)+(0)+(ex^e-1)
g'(x)=(e^sinx)(cosx)-csc(e^x)(e^x)

 

[stinajeana]

For f(x), you have a sum of four terms. In the first and second terms, you have numbers to a variable power. Apply the appropriate rule. (Review the list of rules they gave you, if you're not sure.) The third term is just a number. The fourth term is a variable to a numerical power; apply the appropriate rule.

For g(x), you'll need to apply the Chain Rule to each of the two terms. For the first term, you'll start by differentiating the exponential, and then you'll differentiate what is in the exponent. For the second, you'll start by differentiating the trig function; then you'll differentiate the argument of that function.

If you get stuck, please reply showing how far you have gotten for each of the terms. Thank you.

Also,
Wouldn't g'(x)= (lne)e^sinx*(cosx)-[cscx(cotx)*(e^x)]? why do you multiply cscx and cotx by (e^x)?

 

[stinajeana]

For f(x), you have a sum of four terms. In the first and second terms, you have numbers to a variable power. Apply the appropriate rule. (Review the list of rules they gave you, if you're not sure.) The third term is just a number. The fourth term is a variable to a numerical power; apply the appropriate rule.

For g(x), you'll need to apply the Chain Rule to each of the two terms. For the first term, you'll start by differentiating the exponential, and then you'll differentiate what is in the exponent. For the second, you'll start by differentiating the trig function; then you'll differentiate the argument of that function.

If you get stuck, please reply showing how far you have gotten for each of the terms. Thank you.

Haha ok, nevermind. I just went through it again and realized what I did wrong.

 

[HallsofIvy]

Calculus 1 in university. I GET IT, I'm an idiot because I have not studied precalculus.

so how do i differentiate e^pi and x^e?

should I be doing each term individually?

That's a strange thing to say. mmm4444bot asked what class you are in to get a better idea of what hints would most help. In Calculus I, you should have learned that the derivative of \(\displaystyle x^n\) is \(\displaystyle nx^{n-1}\). And that applies for n any number, not just integers. As for \(\displaystyle e^{\pi}\), do you see that there is no variable "x" in the formula? \(\displaystyle e^{\pi}\) is a constant.