Solve 3t*5t

$$3 t \times 5 t$$

Evaluate

$$15t^{2}$$

Solution Steps

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

$$3t^{2}\times 5$$

Multiply 3 and 5 to get 15.

$$15t^{2}$$

Differentiate w.r.t. t

$$30t$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(3t^{2}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}t}(15t^{2})$$

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

$$2\times 15t^{2-1}$$

Multiply 2 times 15.

$$30t^{2-1}$$

Subtract 1 from 2.

$$30t^{1}$$

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

$$30t$$