I'm on a workbook problem and I want to make sure I'm doing it properly. The problem asks me to find the derivatives of composite functions when given only the graphs of the original functions, here are my steps:
I am supposed to find the derivative of $A'(1)$ where $A$ is a composite function in the form of $F(G(X))$.
I start off by rendering the derivative of the composite, which renders as: $$f'(g(1)) * g'(1)$$
I look at the graph and find that $g(1)$ equals $3$.
$$f'(3) * g'(1)$$
Next I look at the slope of the tangent at $f(3)$ and estimate it to be at $-\frac{1}{4}$.
$$-\frac{1}{4}*g'(1)$$
Next I look at the slope of the tangent at $g(1)$ and estimate it to be $-3$.
$$-\frac{1}{4}*-3 = \frac{3}{4}$$
So have I reached the right conclusion?