Solve 9y^3/3y

$$\frac { 9 y ^ { 3 } } { 3 y }$$

Evaluate

$$3y^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}y^{3}}{3^{1}y^{1}}$$

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

$$\frac{9^{1}y^{3-1}}{3^{1}}$$

Subtract 1 from 3.

$$\frac{9^{1}y^{2}}{3^{1}}$$

Divide 9 by 3.

$$3y^{2}$$

Differentiate w.r.t. y

$$6y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{9}{3}y^{3-1})$$

Do the arithmetic.

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

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}.

$$2\times 3y^{2-1}$$

Do the arithmetic.

$$6y^{1}$$

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

$$6y$$