Solve s(3/2)(-2/5)(-5/8)

$$s ( \frac { 3 } { 2 } ) ( - \frac { 2 } { 5 } ) ( - \frac { 5 } { 8 } )$$

Evaluate

$$\frac{3s}{8}$$

Solution Steps

Multiply \frac{3}{2} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$s\times \frac{3\left(-2\right)}{2\times 5}\left(-\frac{5}{8}\right)$$

Do the multiplications in the fraction \frac{3\left(-2\right)}{2\times 5}.

$$s\times \frac{-6}{10}\left(-\frac{5}{8}\right)$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

$$s\left(-\frac{3}{5}\right)\left(-\frac{5}{8}\right)$$

Multiply -\frac{3}{5} times -\frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$s\times \frac{-3\left(-5\right)}{5\times 8}$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{5\times 8}.

$$s\times \frac{15}{40}$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$s\times \frac{3}{8}$$

Differentiate w.r.t. s

$$\frac{3}{8} = 0.375$$

Steps Using Definition of a Derivative

Multiply \frac{3}{2} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\times \frac{3\left(-2\right)}{2\times 5}\left(-\frac{5}{8}\right))$$

Do the multiplications in the fraction \frac{3\left(-2\right)}{2\times 5}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\times \frac{-6}{10}\left(-\frac{5}{8}\right))$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\left(-\frac{3}{5}\right)\left(-\frac{5}{8}\right))$$

Multiply -\frac{3}{5} times -\frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\times \frac{-3\left(-5\right)}{5\times 8})$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{5\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\times \frac{15}{40})$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}s}(s\times \frac{3}{8})$$

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

$$\frac{3}{8}s^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{8}s^{0}$$

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

$$\frac{3}{8}\times 1$$

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

$$\frac{3}{8}$$