Solve x+2/3x+5/6x

$$x+ \frac{ 2 }{ 3 } x+ \frac{ 5 }{ 6 } x$$

Evaluate

$$\frac{5x}{2}$$

Solution Steps

Combine x and \frac{2}{3}x to get \frac{5}{3}x.

$$\frac{5}{3}x+\frac{5}{6}x$$

Combine \frac{5}{3}x and \frac{5}{6}x to get \frac{5}{2}x.

$$\frac{5}{2}x$$

Differentiate w.r.t. x

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps Using Definition of a Derivative

Combine x and \frac{2}{3}x to get \frac{5}{3}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{3}x+\frac{5}{6}x)$$

Combine \frac{5}{3}x and \frac{5}{6}x to get \frac{5}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{2}x)$$

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

$$\frac{5}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{2}x^{0}$$

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

$$\frac{5}{2}\times 1$$

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

$$\frac{5}{2}$$