Solve 25y^4/5y

$$\frac { 25 y ^ { 4 } } { 5 y }$$

Evaluate

$$5y^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{25^{1}y^{4}}{5^{1}y^{1}}$$

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

$$\frac{25^{1}y^{4-1}}{5^{1}}$$

Subtract 1 from 4.

$$\frac{25^{1}y^{3}}{5^{1}}$$

Divide 25 by 5.

$$5y^{3}$$

Differentiate w.r.t. y

$$15y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{25}{5}y^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{3})$$

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}.

$$3\times 5y^{3-1}$$

Do the arithmetic.

$$15y^{2}$$