Solve (1*10^-4cm)*(0.4*15^-4cm)/4*10^-9cm^2

$$\frac { ( 1 \times 10 ^ { - 4 } cm ) \times ( 0.4 \times 15 ^ { - 4 } cm ) } { 4 \times 10 ^ { - 9 } cm ^ { 2 } }$$

Evaluate

$$\frac{16c}{81}$$

Solution Steps

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

$$\frac{1\times 10^{-4}c^{2}m\times 0.4\times 15^{-4}m}{4\times 10^{-9}cm^{2}}$$

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

$$\frac{1\times 10^{-4}c^{2}m^{2}\times 0.4\times 15^{-4}}{4\times 10^{-9}cm^{2}}$$

Cancel out cm^{2} in both numerator and denominator.

$$\frac{0.4\times 10^{-4}\times 15^{-4}c}{4\times 10^{-9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{0.4\times 10^{5}\times 15^{-4}c}{4}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{0.4\times 100000\times 15^{-4}c}{4}$$

Multiply 0.4 and 100000 to get 40000.

$$\frac{40000\times 15^{-4}c}{4}$$

Calculate 15 to the power of -4 and get \frac{1}{50625}.

$$\frac{40000\times \frac{1}{50625}c}{4}$$

Multiply 40000 and \frac{1}{50625} to get \frac{64}{81}.

$$\frac{\frac{64}{81}c}{4}$$

Divide \frac{64}{81}c by 4 to get \frac{16}{81}c.

$$\frac{16}{81}c$$

Differentiate w.r.t. c

$$\frac{16}{81} = 0.19753086419753085$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{2cmm}{2531250000\times \frac{4m^{2}}{1000000000}}c^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{16c}{81}c^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{16c}{81})$$

The derivative of a constant term is 0.

$$0$$