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!

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- Feb 19th 2009, 11:48 PMkatieeejcomplicated logarithmic differentiation
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! - Feb 20th 2009, 01:51 AMtom@ballooncalculus
Hi katieeej -

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

http://www.ballooncalculus.org/asy/diffChain/sinSqd.png

...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...

http://www.ballooncalculus.org/chain_rule.png

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

Don't integrate - balloontegrate!

Balloon Calculus: worked examples from past papers - Feb 20th 2009, 01:59 AMkatieeejclarification
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. - Feb 20th 2009, 02:46 AMtom@ballooncalculus
http://www.ballooncalculus.org/asy/d...in/logXsqd.png

More in a moment... - Feb 20th 2009, 03:05 AMtom@ballooncalculus
Then the product rule...

http://www.ballooncalculus.org/asy/d...mesLogQuad.png

And then you need to apply the chain rule to $\displaystyle \ln | \sin^2 x |$... - Feb 20th 2009, 03:16 AMtom@ballooncalculus
And using the derivative of $\displaystyle \sin^2 x$ which is the same as that of $\displaystyle \sin^2 x + 5$ in the first picture...

http://www.ballooncalculus.org/asy/d...logSinXsqd.png

Don't integrate - balloontegrate!

Balloon Calculus: worked examples from past papers