Can someone help me with math?
Just started doing derivatives and I only know the basic rules (sum/difference of derivatives, product, quotient rule, I don't know chain rule) and I can't seem to get the right answer to this question. Can anyone point me where I'm wrong?
f(x) = [3(1 - sin(x))] / (2cos(x))
(Distributed the 3 over the (1 - sin(x))
> (3 - 3sin(x)) / (2cos(x))
(Rewrote the function as two fractions)
> (3/2)(1/cos(x)) - (3/2)(sin(x)/cos(x))
(Trig identities)
> (3/2)(sec(x)) - (3/2)(tan(x))
(Differentiated here. 3/2 is a constant multiple so I just multiply it with the separate derivatives. I know that d/dx (sec(x)) = sec(x)tan(x) and d/dx (tan(x)) = sec^2(x). Since this is just a difference of two terms, I can just subtract the individual derivatives)
> (3/2)(sec(x)tan(x)) - (3/2)(sec^2(x))
(Factor)
>(3sec(x)/2)(tan(x) - sec(x))
But my book says that's wrong. What am I doing wrong? I'd appreciate the help.
3 Comments • Newest first
@SunsetDews You don't need to spend all those steps rewriting the function; just bring the 3 and 2 out front so you have f(x)=3/2[(1-sinx)/(cosx)] and then use the quotient rule. There's no need to rewrite it as much as you did.
http://www.wolframalpha.com/input/?i=derviative++%5B3%281+-+sin%28x%29%29%5D+%2F+%282cos%28x%29%29+
You're at least right. What does the book say?
I solved it myself just now and I get the same answer as you. What does your book say it is?