APFIVE Rank the following steps to differentiate $$y=\sin\big(e^{2*x}\big)$$ using the chain rule (from first to last):
A) Identify the layers: outer function $$\sin(u)$$ and inner function $$e^{2*x}$$, with an innermost linear function $$2*x$$.
B) Differentiate the outer function to obtain $$\cos\big(e^{2*x}\big)$$.
C) Differentiate the inner function $$e^{2*x}$$, noting its derivative is $$e^{2*x}*2$$.
D) Multiply the derivatives of the outer and inner functions to obtain the final derivative.
Identify the layers: outer $$\sin(u)$$, inner $$e^{2*x}$$, and innermost $$2*x$$; differentiate the outer function to get $$\cos(e^{2*x})$$; differentiate $$e^{2*x}$$ to get $$2*e^{2*x}$$; then multiply the derivatives
Treat $$e^{2*x}$$ as a constant, differentiate $$\sin(u)$$ directly, and then multiply by the derivative of $$2*x$$
Differentiate $$\sin(e^{2*x})$$ and $$e^{2*x}$$ simultaneously, then multiply by 2 afterward, ignoring the nested structure
Differentiate $$e^{2*x}$$ first, then apply the derivative of sine directly without the proper chain rule for $$\sin(u)$$, and multiply by $$2*x$$
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