Solve +4kxdivkx^2

$$+ 4 k x \div k x ^ { 2 }$$

Evaluate

$$4x^{3}$$

Solution Steps

Cancel out k in both numerator and denominator.

$$4xx^{2}$$

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

$$4x^{3}$$

Differentiate w.r.t. x

$$12x^{2}$$

Steps Using Definition of a Derivative

Cancel out k in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4xx^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3})$$

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

$$3\times 4x^{3-1}$$

Multiply 3 times 4.

$$12x^{3-1}$$

Subtract 1 from 3.

$$12x^{2}$$