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Formation of a Differential Equation from a General Solution

y = e xShow ...

Question

$y = e^{x}$
Show that: $\frac{d y}{d x} = e^{x}$

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Solution

By First Principle of Derivation.
${lim}_{h \to 0} (\frac{e^{x + h} - e^{x}}{h}) = {lim}_{h \to 0} e^{x} (\frac{e^{h} - 1}{h}) = e^{x} \cdot 1 = e^{x}$

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