Solve 4x^3/2x

$$\frac { 4 x ^ { 3 } } { 2 x }$$

Evaluate

$$2x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}x^{3}}{2^{1}x^{1}}$$

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

$$\frac{4^{1}x^{3-1}}{2^{1}}$$

Subtract 1 from 3.

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

Divide 4 by 2.

$$2x^{2}$$

Differentiate w.r.t. x

$$4x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{2}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4x^{1}$$

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

$$4x$$