complicated logarithmic differentiation

**katieeej** · February 19th 2009, 11:48 PM

i'm so sorry for keep asking questions but im really confused for this one.
the problem is y=(e^(x-1)*sin^2*x)/(((x^2)+5)^2x)

the trig function (sin^2 + 5), i don't know how to get a derivative out of that.

help me plz!

**tom@ballooncalculus** · February 20th 2009, 01:51 AM

Hi katieeej -

if you mean $\sin^2 x + 5$ then this calls for a simple application of the chain rule for differentiation...

...where straight continuous line differentiate downwards with respect to x and the straight dashed line with respect to the dashed balloon expression, so that the triangular network satisfies the chain rule...

... though I'm not sure you meant \sin^2 x...

Don't integrate - balloontegrate!

Balloon Calculus: worked examples from past papers

**katieeej** · February 20th 2009, 01:59 AM

the equation is

y=

e^(x-1)*sin^2(x)
-------------------- division
(x^2 +5)^2x

i started off like
ln y = ln(e^(x-1)sin^2 (x)) - ln (x^2 +5)^2x
= ln(e^(x-1))+ln (sin^2 (x))- 2x ln (x^2 +5)
= x-1 ln e +ln sin^2 (x) - 2x ln (x^2+5)
=x-1+ln (sin^2 (x)) -2x ln (x^2 +5)

then i don't know how to get derivatives.