Solve x+2x+10/3x+5/3x

$$x+2x+ \frac{ 10 }{ 3 } x+ \frac{ 5 }{ 3 } x$$

Evaluate

$$8x$$

Solution Steps

Combine x and 2x to get 3x.

$$3x+\frac{10}{3}x+\frac{5}{3}x$$

Combine 3x and \frac{10}{3}x to get \frac{19}{3}x.

$$\frac{19}{3}x+\frac{5}{3}x$$

Combine \frac{19}{3}x and \frac{5}{3}x to get 8x.

$$8x$$

Differentiate w.r.t. x

$$8$$

Steps Using Definition of a Derivative

Combine x and 2x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+\frac{10}{3}x+\frac{5}{3}x)$$

Combine 3x and \frac{10}{3}x to get \frac{19}{3}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{19}{3}x+\frac{5}{3}x)$$

Combine \frac{19}{3}x and \frac{5}{3}x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x)$$

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

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$