Solve y^2quady^2*y^3=

$$y ^ { 2 } \quad y ^ { 2 } \cdot y ^ { 3 } =$$

Evaluate

$$y^{7}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{2}y^{2}y^{3}$$

Use the Multiplication Rule for Exponents.

$$y^{2+2+3}$$

Add the exponents 2 and 2.

$$y^{4+3}$$

Add the exponents 4 and 3.

$$y^{7}$$

Differentiate w.r.t. y

$$7y^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{4}y^{3})$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{7})$$

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

$$7y^{7-1}$$

Subtract 1 from 7.

$$7y^{6}$$