Solve 18t/u*u/2

$$\frac { 18 t } { u } \times \frac { u } { 2 }$$

Evaluate

$$9t$$

Solution Steps

Multiply \frac{18t}{u} times \frac{u}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18tu}{u\times 2}$$

Cancel out 2u in both numerator and denominator.

$$9t$$

Differentiate w.r.t. t

$$9$$

Steps Using Definition of a Derivative

Multiply \frac{18t}{u} times \frac{u}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{18tu}{u\times 2})$$

Cancel out 2u in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}t}(9t)$$

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

$$9t^{1-1}$$

Subtract 1 from 1.

$$9t^{0}$$

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

$$9\times 1$$

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

$$9$$