How do I simplify f'(x) into the form -((x+c)/(mx+n))^p?

shiri
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Let f(x) = sqrt(49-x^2) + 7arccos(x/7).

Then f'(x) can be written in the simplified form -((x+c)/(mx+n))^p

What are the values of c, m, n and p?

So far what I got in simplified form is (-x-7)/sqrt(49-x^2)


How can I make my simplified form into that simplified form?
 
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Hi shiri! :smile:

(try using the X2 tag just above the Reply box :wink:)

Hint: 49 - x2 = (7 + x)(7 - x) :smile:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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