Solve 2/15text{u}5/12

$$\frac { 2 } { 15 } \text { u } \frac { 5 } { 12 }$$

Evaluate

$$\frac{u}{18}$$

Solution Steps

Multiply \frac{2}{15} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 5}{15\times 12}u$$

Do the multiplications in the fraction \frac{2\times 5}{15\times 12}.

$$\frac{10}{180}u$$

Reduce the fraction \frac{10}{180} to lowest terms by extracting and canceling out 10.

$$\frac{1}{18}u$$

Differentiate w.r.t. u

$$\frac{1}{18} = 0.05555555555555555$$

Steps Using Definition of a Derivative

Multiply \frac{2}{15} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{2\times 5}{15\times 12}u)$$

Do the multiplications in the fraction \frac{2\times 5}{15\times 12}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{10}{180}u)$$

Reduce the fraction \frac{10}{180} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{18}u)$$

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

$$\frac{1}{18}u^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{18}u^{0}$$

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

$$\frac{1}{18}\times 1$$

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

$$\frac{1}{18}$$