Solve y^5y^9/yy^5

$$\frac { y ^ { 5 } y ^ { 9 } } { y y ^ { 5 } }$$

Evaluate

$$y^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{y^{14}}{yy^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{y^{14}}{y^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$y^{8}$$

Differentiate w.r.t. y

$$8y^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{14}}{yy^{5}})$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{14}}{y^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8y^{8-1}$$

Subtract 1 from 8.

$$8y^{7}$$