Solve y^10divy^5=

$$y ^ { 10 } \div y ^ { 5 } =$$

Evaluate

$$y^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{10}}{y^{5}}$$

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

$$y^{10-5}$$

Subtract 5 from 10.

$$y^{5}$$

Differentiate w.r.t. y

$$5y^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{10-5})$$

Do the arithmetic.

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

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}.

$$5y^{5-1}$$

Do the arithmetic.

$$5y^{4}$$