Solve 4cm1/4cm1/10cm

$$4 cm \frac { 1 } { 4 cm } \frac { 1 } { 10 cm }$$

Evaluate

$$\frac{1}{10cm}$$

Solution Steps

Express 4\times \frac{1}{4cm} as a single fraction.

$$\frac{4}{4cm}cm\times \frac{1}{10cm}$$

Multiply \frac{4}{4cm} times \frac{1}{10cm} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{4cm\times 10cm}cm$$

Multiply c and c to get c^{2}.

$$\frac{4}{4c^{2}m\times 10m}cm$$

Multiply m and m to get m^{2}.

$$\frac{4}{4c^{2}m^{2}\times 10}cm$$

Multiply 4 and 10 to get 40.

$$\frac{4}{40c^{2}m^{2}}cm$$

Express \frac{4}{40c^{2}m^{2}}c as a single fraction.

$$\frac{4c}{40c^{2}m^{2}}m$$

Cancel out 4c in both numerator and denominator.

$$\frac{1}{10cm^{2}}m$$

Express \frac{1}{10cm^{2}}m as a single fraction.

$$\frac{m}{10cm^{2}}$$

Cancel out m in both numerator and denominator.

$$\frac{1}{10cm}$$

Differentiate w.r.t. c

$$-\frac{1}{10mc^{2}}$$