Consider a function,
$$y=arcsin(x)$$ When differentiation is done implicitly it gives $$dy/d x=1/cosy-------(1)$$ And if differentiation is done explicitly it gives $$dy/dx=1/√(1-x^2)$$ I want to know if they will make same graph in coordinate axes ? I cannot di it myself because i dont know what value i should put in eqn (1) to graph it. Help would be greatly appreciated.
Notice that since $y=\arcsin (x)$, we have $\cos y=cos(\arcsin (x))$ . To compute the trig function of an arctrig function, we set up a right triangle to take us from the original side ($x$), to the associated angle ($\arcsin (x)$, then find the $\cos$ of that angle.
So, $\sin$ is $\frac {\text{opposite}} {\text{hypotenuse}}=\frac x 1$, this makes the adjacent side $\sqrt{1-x^2}$. Then $$\cos (y)=\cos(\arcsin(x))=\frac {\text{adjacent}} {\text{hypotenuse}}=\frac {\sqrt{1-x^2}}1={\sqrt{1-x^2}}$$
So for points on your curve, the two are equivalent