Find derivative at 1 of this complicated function

sa1
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Homework Statement


find dy/dx at x=-1 .

Homework Equations


sin ysin pi*x/2 + 31/2/2(sec-12x) +2x(tan(ln(x+2)))=0

The Attempt at a Solution


There is coming a term ln(sin pi*x/2) during differentiation which will be a ln of a negative number. Sorry if the problem is too easy .I am just starting differentiation.
 
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Is that really \sin (y^\frac{sin \pi x}{2})?
 


no it is (sin y)sin (pi*x/2)
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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