Solve x^6:x^2

$$x ^ { 6 } : x ^ { 2 }$$

Evaluate

$$x^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{6}}{x^{2}}$$

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

$$x^{6-2}$$

Subtract 2 from 6.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{6-2})$$

Do the arithmetic.

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

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}.

$$4x^{4-1}$$

Do the arithmetic.

$$4x^{3}$$