could someone help me find the derive. of this:

*postin

Question

could someone help me find the derive. of this: 



*postin

math2400 · Answer

$$y=(\cos \theta)^\sqrt{2}$$

math2400 · Answer

i thought i could use the formula $$\frac{ d }{ dx } \left[ a^u \right] = (lna)a^u(u')$$ but when i did that i got the wrong answer...this is what i got so far but it's wrong: 

$$y'= \ln \cos \theta (1)(\cos^\sqrt{2})$$

zepdrix · Answer

Notice that the exponent is a CONSTANTTTTTTT.
We don't apply that rule I'm afraid :(
We simply do the power rule.

It will look a bit ugly, but it works!!

zepdrix · Answer

Example:$$\Large \frac{d}{dx}x^{\sqrt3}\quad=\quad \sqrt3 \cdot x^{(\sqrt3-1)}$$
Understand what I mean? :o

math2400 · Answer

ohhh wow. ok so just to make sure, i can only  apply the rule if u is anything but a constant correct? for instance any variable would work

zepdrix · Answer

Mmmm the answer to your question is ... yes.

But be careful with functions like:$$\Large y\quad=\quad x^x$$See how the exponent is a variable?
You would think you can apply the rule here, but nooooo.
Since the base is `also` a variable, we have to do something else to solve this one.
Namely, using logarithms.

math2400 · Answer

oh ok. so can't apply that rule if 
1. u is a constant
2. if a and u are exponents

zepdrix · Answer

1. correct, we simply do the power rule silly! :)
2. if a and u are `variables`, yes ( I think that's what you meant to say lol ).

math2400 · Answer

haha yes that's what i meant! 
thank you so much for clarifying! really helped me out there

zepdrix · Answer

cool \c:/