Solve 2y^3/2y

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

Evaluate

$$y^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 1.

$$2^{0}y^{3-1}$$

For any number a except 0, a^{0}=1.

$$y^{3-1}$$

Subtract 1 from 3.

$$y^{2}$$

Differentiate w.r.t. y

$$2y$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$2y^{2-1}$$

Do the arithmetic.

$$2y^{1}$$

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

$$2y$$