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F ′ (x) = (1 − 4 x) e − 2 x 2 x 8 Explanation The chain rule states that derivative of a function of a function, say d x d f (g (x)) = d g d f ⋅ d x d g How do you differentiate \displaystyle{f{{\left({x}\right)}}}={e}^{{{5}{x}^{{2}}{x}{3}}} using the chain rule?. W{ w U wx r { H ts} r5 r wx {iX 5 yv G v { r w x E s x U x X 5 >O54C@5AOAiU x X H{ x r X X ðXïîìïõl XòXññíïlîì 11 îìíð E { { { 5 w. This means the graph of h(x) crosses the xaxis at the same two points as f(x) and g(x) Thus, if there are points of tangency then they must occur at these common points on the xaxis Experienced students, very bright students, and good problem solvers could whittle this information and a lot more information out of this algebraic analysis.
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