Solve 6000t*e^-05t

$$6000 t \cdot e ^ { - 05 t }$$

Evaluate

$$6000t$$

Solution Steps

Multiply 0 and 5 to get 0.

$$6000te^{0t}$$

Anything times zero gives zero.

$$6000te^{0}$$

Calculate e to the power of 0 and get 1.

$$6000t\times 1$$

Multiply 6000 and 1 to get 6000.

$$6000t$$

Differentiate w.r.t. t

$$6000$$

Steps Using Definition of a Derivative

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6000te^{0t})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6000te^{0})$$

Calculate e to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6000t\times 1)$$

Multiply 6000 and 1 to get 6000.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6000t)$$

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

$$6000t^{1-1}$$

Subtract 1 from 1.

$$6000t^{0}$$

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

$$6000\times 1$$

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

$$6000$$