Evaluating limits with several notations $$\lim_{x\to0} \frac{f(e^{5x} - x^2) - f(1)}{x}$$
It is known that $f'(1) = -2$
Given this info, I'm left with many questions. I'm going to assume that I'll want to substitute for something. I'll let $g(x) = e^{5x} - x^2$. But how do I incorporate the fact that $f'(1) = -2$? Should $g(1) = f'(1)$? 
Also, is the differentiation of g(x) as follows?:
$$f'(e^{5x}-x^2) = 5e^{5x} - 2x $$ 
I figured this is wrong as it's inside the function notation.  

$$\frac{f(e^{5x}-x^{2})-f(1)}{x}=\frac{f(1+e^{5x}-1-x^{2})-f(1)}{e^{5x}-1-x^{2}}\cdot\left(5\cdot\frac{e^{5x}-1}{5x}-x\right)$$ and this tends to $f'(1)\cdot 5=-10$ as $x\to 0$. The use of advanced tools like L'Hospital's Rule and Taylor series are mostly unnecessary for simple limit problems. 
