Solve (y)^5(y)^6(y)=

$$( y ) ^ { 5 } ( y ) ^ { 6 } ( y ) =$$

Evaluate

$$y^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{5}y^{6}y^{1}$$

Use the Multiplication Rule for Exponents.

$$y^{5+6+1}$$

Add the exponents 5 and 6.

$$y^{11+1}$$

Add the exponents 11 and 1.

$$y^{12}$$

Differentiate w.r.t. y

$$12y^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{11}y)$$

To multiply powers of the same base, add their exponents. Add 11 and 1 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{12})$$

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

$$12y^{12-1}$$

Subtract 1 from 12.

$$12y^{11}$$