Solve 12x^2div4x

$$12 x ^ { 2 } \div 4 x$$

Evaluate

$$3x^{3}$$

Solution Steps

Divide 12x^{2} by 4 to get 3x^{2}.

$$3x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3x^{3}$$

Differentiate w.r.t. x

$$9x^{2}$$

Steps Using Definition of a Derivative

Divide 12x^{2} by 4 to get 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}x)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Multiply 3 times 3.

$$9x^{3-1}$$

Subtract 1 from 3.

$$9x^{2}$$