Solve θθθ

$$\theta \theta \theta$$

Evaluate

$$\theta ^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\theta ^{1}\theta ^{1}\theta ^{1}$$

Use the Multiplication Rule for Exponents.

$$\theta ^{1+1+1}$$

Add the exponents 1 and 1.

$$\theta ^{2+1}$$

Add the exponents 2 and 1.

$$\theta ^{3}$$

Differentiate w.r.t. θ

$$3\theta ^{2}$$

Steps Using Definition of a Derivative

Multiply \theta and \theta to get \theta ^{2}.

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

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

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

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

$$3\theta ^{3-1}$$

Subtract 1 from 3.

$$3\theta ^{2}$$