Calculus Examples

$h (x) = - 2 t^{2} + 9 e^{t}$

Step 1

Find the first derivative.

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Step 1.1

By the Sum Rule, the derivative of $- 2 t^{2} + 9 e^{t}$ with respect to $x$ is $\frac{d}{d x} [- 2 t^{2}] + \frac{d}{d x} [9 e^{t}]$ .

$\frac{d}{d x} [- 2 t^{2}] + \frac{d}{d x} [9 e^{t}]$

Step 1.2

Since $- 2 t^{2}$ is constant with respect to $x$ , the derivative of $- 2 t^{2}$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [9 e^{t}]$

Step 1.3

Since $9 e^{t}$ is constant with respect to $x$ , the derivative of $9 e^{t}$ with respect to $x$ is $0$ .

$0 + 0$

Step 1.4

Add $0$ and $0$ .

$f' (x) = 0$

Step 2

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

$f'' (x) = 0$

Step 3

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

$f''' (x) = 0$

Step 4

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

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

Step 5

The fourth derivative of $h (x)$ with respect to $x$ is $0$ .

$0$