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Second derivative of $$$e^{2}$$$
Related calculators: Derivative Calculator, Logarithmic Differentiation Calculator
Your Input
Find $$$\frac{d^{2}}{de^{2}} \left(e^{2}\right)$$$.
Solution
Find the first derivative $$$\frac{d}{de} \left(e^{2}\right)$$$
Apply the power rule $$$\frac{d}{de} \left(e^{n}\right) = n e^{n - 1}$$$ with $$$n = 2$$$:
$${\color{red}\left(\frac{d}{de} \left(e^{2}\right)\right)} = {\color{red}\left(2 e\right)}$$Thus, $$$\frac{d}{de} \left(e^{2}\right) = 2 e$$$.
Next, $$$\frac{d^{2}}{de^{2}} \left(e^{2}\right) = \frac{d}{de} \left(2 e\right)$$$
Apply the constant multiple rule $$$\frac{d}{de} \left(c f{\left(e \right)}\right) = c \frac{d}{de} \left(f{\left(e \right)}\right)$$$ with $$$c = 2$$$ and $$$f{\left(e \right)} = e$$$:
$${\color{red}\left(\frac{d}{de} \left(2 e\right)\right)} = {\color{red}\left(2 \frac{d}{de} \left(e\right)\right)}$$Apply the power rule $$$\frac{d}{de} \left(e^{n}\right) = n e^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{de} \left(e\right) = 1$$$:
$$2 {\color{red}\left(\frac{d}{de} \left(e\right)\right)} = 2 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{de} \left(2 e\right) = 2$$$.
Therefore, $$$\frac{d^{2}}{de^{2}} \left(e^{2}\right) = 2$$$.
Answer
$$$\frac{d^{2}}{de^{2}} \left(e^{2}\right) = 2$$$A