Calculus Examples

$f (x) = 3 - \frac{3}{5 (\frac{3}{5})}$

Step 1

Differentiate.

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Step 1.1

Combine $5$ and $\frac{3}{5}$ .

$\frac{d}{d x} [3 - \frac{3}{\frac{5 \cdot 3}{5}}]$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $5$ by $3$ .

$\frac{d}{d x} [3 - \frac{3}{\frac{15}{5}}]$

Step 1.2.2

Divide $15$ by $5$ .

$\frac{d}{d x} [3 - \frac{3}{3}]$

Step 1.2.3

Divide $3$ by $3$ .

$\frac{d}{d x} [3 - 1 \cdot 1]$

Step 1.3

By the Sum Rule, the derivative of $3 - 1 \cdot 1$ with respect to $x$ is $\frac{d}{d x} [3] + \frac{d}{d x} [- 1 \cdot 1]$ .

$\frac{d}{d x} [3] + \frac{d}{d x} [- 1 \cdot 1]$

Step 1.4

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 1 \cdot 1]$

Step 2

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

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Step 2.1

Multiply $- 1$ by $1$ .

$0 + \frac{d}{d x} [- 1]$

Step 2.2

Since $- 1$ is constant with respect to $x$ , the derivative of $- 1$ with respect to $x$ is $0$ .

$0 + 0$

Step 3

Add $0$ and $0$ .

$0$