Solve y*y^5*y^5*y

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

Evaluate

$$y^{12}$$

Solution Steps

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

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

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

$$y^{11}y$$

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

$$y^{12}$$

Differentiate w.r.t. y

$$12y^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{6}y^{5}y)$$

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

$$12y^{11}$$