# Simple Differentiation (checking i'm right)

• Nov 18th 2009, 11:51 PM
aceband
Simple Differentiation (checking i'm right)
Hi,

I'm just doing a past paper but i don't have the mark scheme would anyone be kind enough to double check my answer:

Question: Differentiate $\displaystyle (e^x)/(sin(x) + cos(x))$

MyAnswer: $\displaystyle (e^x(sin(x) + cos(x)) + e^x(cos(x) - sin(x)))/((sin(x) + cos(x))^2)$
• Nov 18th 2009, 11:55 PM
RockHard
Seems correct, you can also simplify this
• Nov 19th 2009, 12:03 AM
aceband
Argh dam it i thought you might be able to - i can't for the life of me see where but it just 'looks' like it should? Could you start me off?
• Nov 19th 2009, 12:22 AM
RockHard
Well for starters in the denominator when you multiply the term
$\displaystyle {(sin(x)+cos(x))}^2$
You can remember the identity $\displaystyle sin(x)^2+cos(x)^2 = 1$
• Nov 19th 2009, 12:34 AM
mr fantastic
Quote:

Originally Posted by aceband and reformatted by Mr F
Hi,

I'm just doing a past paper but i don't have the mark scheme would anyone be kind enough to double check my answer:

Question: Differentiate $\displaystyle \frac{e^x}{\sin(x) + \cos(x)}$

MyAnswer: $\displaystyle \frac{e^x(\sin(x) + \cos(x)) {\color{red}+} e^x(\cos(x) - \sin(x))}{(\sin(x) + \cos(x))^2}$

The red plus should be a minus.

There is a common factor in the numerator which leads to considerable simplification (after you fix the mistake). I'd leave the denominator as it is.