For explicit functions I can calculate the derivative at a certian point using the original function: $$\frac{f(1+0.1) - f(1)}{0.1}$$
And then use $\frac{d}{dx}f(1)$ to check if the function is correct. But what can I do for implicit funcions? how can I calculate the change then compare it with my derivative function
Edit: for example if I was asked to differentiate $f(x)=x^2+\tanh(x)$ and if I am unsure about my answer I could type in on the calculator: $$\frac{f(5+0.000001) - f(5)}{0.000001}$$ and then check my $\frac{d}{dx}f(5)$ they should be approximately equal. My question is if I have an implicit function like $$xy^3=\tan(x+2y)-(x^2-1)$$ and after I differentiate it how can I check if it is correct