Solve y^4*y^-3*y

$$y ^ { 4 } \times y ^ { - 3 } \times y$$

Evaluate

$$y^{2}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{4}y^{-3}y^{1}$$

Use the Multiplication Rule for Exponents.

$$y^{4-3+1}$$

Add the exponents 4 and -3.

$$y^{1+1}$$

Add the exponents 1 and 1.

$$y^{2}$$

Differentiate w.r.t. y

$$2y$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{1}y)$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2})$$

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

$$2y^{2-1}$$

Subtract 1 from 2.

$$2y^{1}$$

For any term t, t^{1}=t.

$$2y$$