1. ## Tricky derivative problem!

I understand how to take the derivative of an equation with respect to a variable, say S, but what do I do when there are two variables involved? Here's the problem d/dx [3cos(x^2) - 4e^t]

2. ## Re: Tricky derivative problem!

Treat t as constant, so
d/dx [3cos(x^2) - 4e^t]
= 3 d/dx cos(x^2) - 4 d/dx e^t
= -6x sin(x^2) - 4e^t x

3. ## Re: Tricky derivative problem!

Originally Posted by Kanwar245
Treat t as constant
Correct. But then...

, so

d/dx [3cos(x^2) - 4e^t]
= 3 d/dx cos(x^2) - 4 d/dx e^t
... the e^t is constant, so it might as well come out with the 4:

= 3 d/dx cos(x^2) - 4e^t d/dx 1

... but then the whole second term is a constant term and drops out...

= -6x sin(x^2)

... period.

As long as t isn't a function of x, or anything... the context of the problem here would help.

4. ## Re: Tricky derivative problem!

What would it look like if t was a function of x?

5. ## Re: Tricky derivative problem!

my bad, I integrated the 2nd part!

6. ## Re: Tricky derivative problem!

Originally Posted by NotAMathmatician314
What would it look like if t was a function of x?
then you'd need to use the chain rule.