# differentiate

• Feb 16th 2008, 12:07 AM
b00yeah05
differentiate
hmmm i think im doing it correctly but im not quite sure and i dont know how to simplify trig terms...help please...

$\displaystyle (5 - cos x) / (5 + sin x)$

I got this far by using the quotient rule...am i correct so far???
---> $\displaystyle (sin x( 5 + sinx) - (5-cos x)cos x ) / 5 + sin^2x$

Also another question......

Find f'
f(x) = $\displaystyle sin^2 x + cos^2 x$

i got .... $\displaystyle 2 sin x . cos x + 2 cos x . -sin x$

correct??

how would i simplify it?
• Feb 16th 2008, 12:45 AM
earboth
Quote:

Originally Posted by b00yeah05
hmmm i think im doing it correctly but im not quite sure and i dont know how to simplify trig terms...help please...

$\displaystyle (5 - cos x) / (5 + sin x)$

I got this far by using the quotient rule...am i correct so far???
---> $\displaystyle (sin x( 5 + sinx) - (5-cos x)cos x ) / 5 + sin^2x$

Also another question......
Find f'
f(x) = $\displaystyle sin^2 x + cos^2 x$
i got .... $\displaystyle 2 sin x . cos x + 2 cos x . -sin x$

#1: Expand the brackets in the numerator. The denominator should read $\displaystyle (5+\sin(x))^2$

#2. If the wording of this question is correct then someone has made a practical joke:

Since $\displaystyle (\sin(x))^2 + (\cos(x))^2 = 1$ the first derivative should be zero:

$\displaystyle f'(x)=2\sin(x) \cdot \cos(x) + 2(-\sin(x)) \cdot \cos(x) = 2\sin(x) \cdot \cos(x) - 2\sin(x) \cdot \cos(x) = 0$