Solve t*t*t*t

$$t \times t \times t \times t$$

Evaluate

$$t^{4}$$

Solution Steps

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

$$t^{2}tt$$

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

$$t^{3}t$$

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

$$t^{4}$$

Differentiate w.r.t. t

$$4t^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{2}tt)$$

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{4})$$

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

$$4t^{4-1}$$

Subtract 1 from 4.

$$4t^{3}$$