Solve y^3*y^7*y

$$y ^ { 3 } \cdot y ^ { 7 } \cdot y$$

Evaluate

$$y^{11}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{3}y^{7}y^{1}$$

Use the Multiplication Rule for Exponents.

$$y^{3+7+1}$$

Add the exponents 3 and 7.

$$y^{10+1}$$

Add the exponents 10 and 1.

$$y^{11}$$

Differentiate w.r.t. y

$$11y^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

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

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

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

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

$$11y^{11-1}$$

Subtract 1 from 11.

$$11y^{10}$$