Solve x+2x+12x

$$x + 2 x + 12 x$$

Evaluate

$$15x$$

Solution Steps

Combine x and 2x to get 3x.

$$3x+12x$$

Combine 3x and 12x to get 15x.

$$15x$$

Differentiate w.r.t. x

$$15$$

Steps Using Definition of a Derivative

Combine x and 2x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+12x)$$

Combine 3x and 12x to get 15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x)$$

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

$$15x^{1-1}$$

Subtract 1 from 1.

$$15x^{0}$$

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

$$15\times 1$$

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

$$15$$