Solve y*y^7*y^5

$$y \cdot y ^ { 7 } \cdot y ^ { 5 }$$

Evaluate

$$y^{13}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{1}y^{7}y^{5}$$

Use the Multiplication Rule for Exponents.

$$y^{1+7+5}$$

Add the exponents 1 and 7.

$$y^{8+5}$$

Add the exponents 8 and 5.

$$y^{13}$$

Differentiate w.r.t. y

$$13y^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{8}y^{5})$$

To multiply powers of the same base, add their exponents. Add 8 and 5 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{13})$$

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

$$13y^{13-1}$$

Subtract 1 from 13.

$$13y^{12}$$