Solve 6/1x+2/10x

$$\frac { 6 } { 1 } x + \frac { 2 } { 10 } x$$

Evaluate

$$\frac{31x}{5}$$

Solution Steps

Anything divided by one gives itself.

$$6x+\frac{2}{10}x$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$6x+\frac{1}{5}x$$

Combine 6x and \frac{1}{5}x to get \frac{31}{5}x.

$$\frac{31}{5}x$$

Differentiate w.r.t. x

$$\frac{31}{5} = 6\frac{1}{5} = 6.2$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+\frac{2}{10}x)$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+\frac{1}{5}x)$$

Combine 6x and \frac{1}{5}x to get \frac{31}{5}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{31}{5}x)$$

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

$$\frac{31}{5}x^{1-1}$$

Subtract 1 from 1.

$$\frac{31}{5}x^{0}$$

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

$$\frac{31}{5}\times 1$$

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

$$\frac{31}{5}$$