Solve III

$$I I I$$

Evaluate

$$I^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$I^{1}I^{1}I^{1}$$

Use the Multiplication Rule for Exponents.

$$I^{1+1+1}$$

Add the exponents 1 and 1.

$$I^{2+1}$$

Add the exponents 2 and 1.

$$I^{3}$$

Differentiate w.r.t. I

$$3I^{2}$$

Steps Using Definition of a Derivative

Multiply I and I to get I^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}I}(I^{3})$$

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

$$3I^{3-1}$$

Subtract 1 from 3.

$$3I^{2}$$