Solve 5cd/14*7/30c

$$\frac { 5 c d } { 14 } \times \frac { 7 } { 30 c }$$

Evaluate

$$\frac{d}{12}$$

Solution Steps

Multiply \frac{5cd}{14} times \frac{7}{30c} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5cd\times 7}{14\times 30c}$$

Cancel out 5\times 7c in both numerator and denominator.

$$\frac{d}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{d}{12}$$

Differentiate w.r.t. d

$$\frac{1}{12} = 0.08333333333333333$$

Steps Using Definition of a Derivative

Multiply \frac{5cd}{14} times \frac{7}{30c} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{5cd\times 7}{14\times 30c})$$

Cancel out 5\times 7c in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{2\times 6})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d}{12})$$

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

$$\frac{1}{12}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{12}d^{0}$$

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

$$\frac{1}{12}\times 1$$

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

$$\frac{1}{12}$$