Calc.
posted by Chelsea .
Differentiate.
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)^(x1) * (sin x)
=  x sin(x)cos^(x1)(x)
(dy/dx)(dx/du)= [(cos^x(x))(ln(cos(x)))(x sin(x)cos^(x1)(x)]
(dy/du)= cos^x(x)*(ln(cos(x)))(x tan(x))
Is this correct?
Also, I am stuck on a different problem.
Differentiate.
y= arctan(arcsin(sqrt(x)))
u= arcsin(sqrt(x))
du= (1/(sqrt(1x^2))) dx
ln y = ln ?? do I put the whole original here?
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