Solve 12ax^2/4ax

$$\frac { 12 a x ^ { 2 } } { 4 a x }$$

Evaluate

$$3x$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}a^{1}x^{2}}{4^{1}a^{1}x^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{12^{1}}{4^{1}}a^{1-1}x^{2-1}$$

Subtract 1 from 1.

$$\frac{12^{1}}{4^{1}}a^{0}x^{2-1}$$

For any number a except 0, a^{0}=1.

$$\frac{12^{1}}{4^{1}}x^{2-1}$$

Subtract 1 from 2.

$$\frac{12^{1}}{4^{1}}x^{1}$$

Divide 12 by 4.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

Cancel out 4ax in both numerator and denominator.

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

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$