Solve x+12x/1000=

$$x + \frac { 12 x } { 1000 } =$$

Evaluate

$$\frac{253x}{250}$$

Solution Steps

Divide 12x by 1000 to get \frac{3}{250}x.

$$x+\frac{3}{250}x$$

Combine x and \frac{3}{250}x to get \frac{253}{250}x.

$$\frac{253}{250}x$$

Differentiate w.r.t. x

$$\frac{253}{250} = 1\frac{3}{250} = 1.012$$

Steps Using Definition of a Derivative

Divide 12x by 1000 to get \frac{3}{250}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{3}{250}x)$$

Combine x and \frac{3}{250}x to get \frac{253}{250}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{253}{250}x)$$

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

$$\frac{253}{250}x^{1-1}$$

Subtract 1 from 1.

$$\frac{253}{250}x^{0}$$

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

$$\frac{253}{250}\times 1$$

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

$$\frac{253}{250}$$