Calculus Examples

$y = e^{k \tan (\sqrt{3})}$

Step 1

Differentiate using the chain rule, which states that $\frac{d}{d k} [f (g (k))]$ is $f' (g (k)) g' (k)$ where $f (k) = e^{k}$ and $g (k) = k \tan (\sqrt{3})$ .

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Step 1.1

To apply the Chain Rule, set $u$ as $k \tan (\sqrt{3})$ .

$\frac{d}{d u} [e^{u}] \frac{d}{d k} [k \tan (\sqrt{3})]$

Step 1.2

Differentiate using the Exponential Rule which states that $\frac{d}{d u} [a^{u}]$ is $a^{u} \ln (a)$ where $a$ = $e$ .

$e^{u} \frac{d}{d k} [k \tan (\sqrt{3})]$

Step 1.3

Replace all occurrences of $u$ with $k \tan (\sqrt{3})$ .

$e^{k \tan (\sqrt{3})} \frac{d}{d k} [k \tan (\sqrt{3})]$

Step 2

Evaluate $\tan (\sqrt{3})$ .

$e^{k \tan (\sqrt{3})} \frac{d}{d k} [k \cdot - 6.14753316]$

Step 3

Move $- 6.14753316$ to the left of $k$ .

$e^{k \tan (\sqrt{3})} \frac{d}{d k} [- 6.14753316 \cdot k]$

Step 4

Since $- 6.14753316$ is constant with respect to $k$ , the derivative of $- 6.14753316 k$ with respect to $k$ is $- 6.14753316 \frac{d}{d k} [k]$ .

$e^{k \tan (\sqrt{3})} (- 6.14753316 \frac{d}{d k} [k])$

Step 5

Differentiate using the Power Rule which states that $\frac{d}{d k} [k^{n}]$ is $n k^{n - 1}$ where $n = 1$ .

$e^{k \tan (\sqrt{3})} (- 6.14753316 \cdot 1)$

Step 6

Multiply $- 6.14753316$ by $1$ .

$e^{k \tan (\sqrt{3})} \cdot - 6.14753316$

Step 7

Move $- 6.14753316$ to the left of $e^{k \tan (\sqrt{3})}$ .

$- 6.14753316 e^{k \tan (\sqrt{3})}$