Calculus Examples

$f (x) = \cos (π) x$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$\frac{d}{d x} [- \cos (0) x]$

Step 2

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

$\frac{d}{d x} [- 1 \cdot 1 x]$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $1$ .

$\frac{d}{d x} [- 1 x]$

Step 3.2

Rewrite $- 1 x$ as $- x$ .

$\frac{d}{d x} [- x]$

Step 4

Since $- 1$ is constant with respect to $x$ , the derivative of $- x$ with respect to $x$ is $- \frac{d}{d x} [x]$ .

$- \frac{d}{d x} [x]$

Step 5

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

$- 1 \cdot 1$

Step 6

Multiply $- 1$ by $1$ .

$- 1$