Solve 12xdiv6x/x+6

$$12 x \div \frac { 6 x } { x + 6 }$$

Evaluate

$$2\left(x+6\right)$$

Solution Steps

Divide 12x by \frac{6x}{x+6} by multiplying 12x by the reciprocal of \frac{6x}{x+6}.

$$\frac{12x\left(x+6\right)}{6x}$$

Cancel out 6x in both numerator and denominator.

$$2\left(x+6\right)$$

Use the distributive property to multiply 2 by x+6.

$$2x+12$$

Differentiate w.r.t. x

$$2$$

Steps Using Derivative Rule for Sum

Divide 12x by \frac{6x}{x+6} by multiplying 12x by the reciprocal of \frac{6x}{x+6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x\left(x+6\right)}{6x})$$

Cancel out 6x in both numerator and denominator.

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

Use the distributive property to multiply 2 by x+6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+12)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2x^{1-1}$$

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$