Solve y^6:y^3

$$y ^ { 6 } : y ^ { 3 }$$

Evaluate

$$y^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{6}}{y^{3}}$$

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

$$y^{6-3}$$

Subtract 3 from 6.

$$y^{3}$$

Differentiate w.r.t. y

$$3y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{6-3})$$

Do the arithmetic.

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

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}.

$$3y^{3-1}$$

Do the arithmetic.

$$3y^{2}$$