Calculus Examples

$5 e^{- x} - 6 e^{- 5 x}$

Step 1

Find the first derivative.

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Step 1.1

By the Sum Rule, the derivative of $5 e^{- x} - 6 e^{- 5 x}$ with respect to $e$ is $\frac{d}{d e} [5 e^{- x}] + \frac{d}{d e} [- 6 e^{- 5 x}]$ .

$\frac{d}{d e} [5 e^{- x}] + \frac{d}{d e} [- 6 e^{- 5 x}]$

Step 1.2

Since $5 e^{- x}$ is constant with respect to $e$ , the derivative of $5 e^{- x}$ with respect to $e$ is $0$ .

$0 + \frac{d}{d e} [- 6 e^{- 5 x}]$

Step 1.3

Since $- 6 e^{- 5 x}$ is constant with respect to $e$ , the derivative of $- 6 e^{- 5 x}$ with respect to $e$ is $0$ .

$0 + 0$

Step 1.4

Add $0$ and $0$ .

$f' (e) = 0$

Step 2

Since $0$ is constant with respect to $e$ , the derivative of $0$ with respect to $e$ is $0$ .

$f'' (e) = 0$

Step 3

Since $0$ is constant with respect to $e$ , the derivative of $0$ with respect to $e$ is $0$ .

$f''' (e) = 0$

Step 4

Since $0$ is constant with respect to $e$ , the derivative of $0$ with respect to $e$ is $0$ .

$f^{4} (e) = 0$