Calculus Examples

$\frac{d}{d t} (a t^{2} + b t + c)$

Step 1

By the Sum Rule, the derivative of $a t^{2} + b t + c$ with respect to $d$ is $\frac{d}{d \cdot d} [a t^{2}] + \frac{d}{d \cdot d} [b t] + \frac{d}{d \cdot d} [c]$ .

$\frac{d}{d \cdot d} [a t^{2}] + \frac{d}{d \cdot d} [b t] + \frac{d}{d \cdot d} [c]$

Step 2

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

$0 + \frac{d}{d \cdot d} [b t] + \frac{d}{d \cdot d} [c]$

Step 3

Since $b t$ is constant with respect to $d$ , the derivative of $b t$ with respect to $d$ is $0$ .

$0 + 0 + \frac{d}{d \cdot d} [c]$

Step 4

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

$0 + 0 + 0$

Step 5

Combine terms.

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Step 5.1

Add $0$ and $0$ .

$0 + 0$

Step 5.2

Add $0$ and $0$ .

$0$