Posted by Chelsea on Wednesday, March 9, 2011 at 4:27pm.
y= (cos x)^x
u= cos x
du= -sin x dx
ln y = ln(cos x)^x
ln y = x ln(cos x)
(dy/dx)/(y)= ln(cos x)
(dy/dx)= y ln(cos x)
= (cos x)^x * (ln cos x)
(dx/du)= x(cos x)^(x-1) * (-sin x)
= - x sin(x)cos^(x-1)(x)
(dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1)(x)]
(dy/du)= cos^x(x)*(ln(cos(x)))-(x tan(x))
Is this correct?
Also, I am stuck on a different problem.
du= (1/(sqrt(1-x^2))) dx
ln y = ln ?? do I put the whole original here?
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