Solve 5000*3.5*6t

$$5000 \cdot 3.5 \cdot 6t$$

Evaluate

$$105000t$$

Solution Steps

Multiply 5000 and 3.5 to get 17500.

$$17500\times 6t$$

Multiply 17500 and 6 to get 105000.

$$105000t$$

Differentiate w.r.t. t

$$105000$$

Steps Using Definition of a Derivative

Multiply 5000 and 3.5 to get 17500.

$$\frac{\mathrm{d}}{\mathrm{d}t}(17500\times 6t)$$

Multiply 17500 and 6 to get 105000.

$$\frac{\mathrm{d}}{\mathrm{d}t}(105000t)$$

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

$$105000t^{1-1}$$

Subtract 1 from 1.

$$105000t^{0}$$

For any term t except 0, t^{0}=1.

$$105000\times 1$$

For any term t, t\times 1=t and 1t=t.

$$105000$$