1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$x : 12 : 7 : 2$$

Evaluate

$\frac{x}{168}$

Solution Steps

Express $\frac{\frac{\frac{x}{12}}{7}}{2}$ as a single fraction.

$$\frac{\frac{x}{12}}{7\times 2}$$

Multiply $7$ and $2$ to get $14$.

$$\frac{\frac{x}{12}}{14}$$

Express $\frac{\frac{x}{12}}{14}$ as a single fraction.

$$\frac{x}{12\times 14}$$

Multiply $12$ and $14$ to get $168$.

$$\frac{x}{168}$$

Show Solution

Differentiate w.r.t. x

$\frac{1}{168} = 0.005952380952380952$

Steps Using Definition of a Derivative

Express $\frac{\frac{\frac{x}{12}}{7}}{2}$ as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{12}}{7\times 2})$$

Multiply $7$ and $2$ to get $14$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{12}}{14})$$

Express $\frac{\frac{x}{12}}{14}$ as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12\times 14})$$

Multiply $12$ and $14$ to get $168$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{168})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{1}{168}x^{1-1}$$

Subtract $1$ from $1$.

$$\frac{1}{168}x^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{1}{168}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{1}{168}$$