Solve DeltaDeltaDelta

$$\Delta \Delta \Delta$$

Evaluate

$$\Delta ^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$\Delta ^{1}\Delta ^{1}\Delta ^{1}$$

Use the Multiplication Rule for Exponents.

$$\Delta ^{1+1+1}$$

Add the exponents 1 and 1.

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

Add the exponents 2 and 1.

$$\Delta ^{3}$$

Differentiate w.r.t. Δ

$$3\Delta ^{2}$$

Steps Using Definition of a Derivative

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

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

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

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

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

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

Subtract 1 from 3.

$$3\Delta ^{2}$$