Solve 2t:1/3

$$2 t : \frac { 1 } { 3 }$$

Evaluate

$$6t$$

Solution Steps

Divide 2t by \frac{1}{3} by multiplying 2t by the reciprocal of \frac{1}{3}.

$$2t\times 3$$

Multiply 2 and 3 to get 6.

$$6t$$

Differentiate w.r.t. t

$$6$$

Steps Using Definition of a Derivative

Divide 2t by \frac{1}{3} by multiplying 2t by the reciprocal of \frac{1}{3}.

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

Multiply 2 and 3 to get 6.

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

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

$$6t^{1-1}$$

Subtract 1 from 1.

$$6t^{0}$$

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

$$6\times 1$$

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

$$6$$