Find the derivative of the function.
I keep on getting a weird answer and I don't think its correct. Sorry that I don't know how to write latex.
y'(x)= 1/2(11+sqrt11+sqrt11)^-1/2 [1+11/2(11+sqrt11)^-1/2 (1+ 11/2x^-1/2)]
Any help is appreciated
Find the derivative of the function.
I keep on getting a weird answer and I don't think its correct. Sorry that I don't know how to write latex.
y'(x)= 1/2(11+sqrt11+sqrt11)^-1/2 [1+11/2(11+sqrt11)^-1/2 (1+ 11/2x^-1/2)]
Any help is appreciated
$\displaystyle y=\sqrt{ax+\sqrt{ax+\sqrt{ax}}}\implies y^2-ax=$$\displaystyle \sqrt{ax+\sqrt{ax}}\implies \left(y^2-ax\right)^2=y^4-2y^2ax+1=$$\displaystyle ax+\sqrt{ax}$. Thus, $\displaystyle 4y^3y''+2yy'ax+2ya=a+\frac{\sqrt{a}}{2\sqrt{x}}$. Doing a little finagling we get $\displaystyle y'=\frac{a-\frac{\sqrt{a}}{2\sqrt{x}}-2ya}{4y^3+2ax}$. Therefore $\displaystyle y'=\frac{a-\frac{\sqrt{a}}{2\sqrt{x}}-2a\sqrt{ax+\sqrt{ax+\sqrt{ax}}}}{4\left(ax+\sqrt{a x+\sqrt{ax}}\right)^{\frac{3}{2}}+2ax}$
you might want to look at this:
derivative of (sqrt (11x + (sqrt (11x +(sqrt 11x - Wolfram|Alpha)))))
I am too slow with latex...