Solve 7/10quadtext{(c)}5/12

$$7 / 10 \quad \text { (c) } 5 / 12$$

Evaluate

$$\frac{7c}{24}$$

Solution Steps

Multiply \frac{7}{10} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{10\times 12}c$$

Do the multiplications in the fraction \frac{7\times 5}{10\times 12}.

$$\frac{35}{120}c$$

Reduce the fraction \frac{35}{120} to lowest terms by extracting and canceling out 5.

$$\frac{7}{24}c$$

Differentiate w.r.t. c

$$\frac{7}{24} = 0.2916666666666667$$

Steps Using Definition of a Derivative

Multiply \frac{7}{10} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{7\times 5}{10\times 12}c)$$

Do the multiplications in the fraction \frac{7\times 5}{10\times 12}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{35}{120}c)$$

Reduce the fraction \frac{35}{120} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{7}{24}c)$$

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

$$\frac{7}{24}c^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{24}c^{0}$$

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

$$\frac{7}{24}\times 1$$

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

$$\frac{7}{24}$$