Solve (-14/36)(-6s/112)

$$( - \frac { 14 } { 36 } ) ( - \frac { 6 s } { 112 } )$$

Evaluate

$$\frac{s}{48}$$

Solution Steps

Reduce the fraction \frac{14}{36} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{18}\left(-\frac{6s}{112}\right)$$

Divide 6s by 112 to get \frac{3}{56}s.

$$-\frac{7}{18}\left(-\frac{3}{56}s\right)$$

Multiply -\frac{7}{18} and -1 to get \frac{7}{18}.

$$\frac{7}{18}\times \frac{3}{56}s$$

Multiply \frac{7}{18} times \frac{3}{56} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{18\times 56}s$$

Do the multiplications in the fraction \frac{7\times 3}{18\times 56}.

$$\frac{21}{1008}s$$

Reduce the fraction \frac{21}{1008} to lowest terms by extracting and canceling out 21.

$$\frac{1}{48}s$$

Differentiate w.r.t. s

$$\frac{1}{48} = 0.020833333333333332$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{14}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}s}(-\frac{7}{18}\left(-\frac{6s}{112}\right))$$

Divide 6s by 112 to get \frac{3}{56}s.

$$\frac{\mathrm{d}}{\mathrm{d}s}(-\frac{7}{18}\left(-\frac{3}{56}s\right))$$

Multiply -\frac{7}{18} and -1 to get \frac{7}{18}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{7}{18}\times \frac{3}{56}s)$$

Multiply \frac{7}{18} times \frac{3}{56} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{7\times 3}{18\times 56}s)$$

Do the multiplications in the fraction \frac{7\times 3}{18\times 56}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{21}{1008}s)$$

Reduce the fraction \frac{21}{1008} to lowest terms by extracting and canceling out 21.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{48}s)$$

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

$$\frac{1}{48}s^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{48}s^{0}$$

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

$$\frac{1}{48}\times 1$$

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

$$\frac{1}{48}$$