Solve y^5*y^6*y^4

$$y ^ { 5 } \cdot y ^ { 6 } \cdot y ^ { 4 }$$

Evaluate

$$y^{15}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{5}y^{6}y^{4}$$

Use the Multiplication Rule for Exponents.

$$y^{5+6+4}$$

Add the exponents 5 and 6.

$$y^{11+4}$$

Add the exponents 11 and 4.

$$y^{15}$$

Differentiate w.r.t. y

$$15y^{14}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{11}y^{4})$$

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{15})$$

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

$$15y^{15-1}$$

Subtract 1 from 15.

$$15y^{14}$$