Calculus Examples

$\sqrt{e^{\cos (2 π)} + \tan (1 + e^{\frac{2}{3}})}$

Step 1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{d}{d x} [\sqrt{e^{\cos (0)} + \tan (1 + e^{\frac{2}{3}})}]$

Step 2

The exact value of $\cos (0)$ is $1$ .

$\frac{d}{d x} [\sqrt{e^{1} + \tan (1 + e^{\frac{2}{3}})}]$

Step 3

Simplify.

$\frac{d}{d x} [\sqrt{e + \tan (1 + e^{\frac{2}{3}})}]$

Step 4

Evaluate $\tan (1 + e^{\frac{2}{3}})$ .

$\frac{d}{d x} [\sqrt{e - 0.19632415}]$

Step 5

Replace with decimal approximation.

$\frac{d}{d x} [\sqrt{2.71828182 - 0.19632415}]$

Step 6

Subtract $0.19632415$ from $2.71828182$ .

$\frac{d}{d x} [\sqrt{2.52195766}]$

Step 7

Since $\sqrt{2.52195766}$ is constant with respect to $x$ , the derivative of $\sqrt{2.52195766}$ with respect to $x$ is $0$ .

$0$