Solve 1.75*10^-4m^3

$$1.75 \cdot 10 ^ { - 4 } m ^ { 3 }$$

Evaluate

$$\frac{7m^{3}}{40000}$$

Solution Steps

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$1.75\times \frac{1}{10000}m^{3}$$

Multiply 1.75 and \frac{1}{10000} to get \frac{7}{40000}.

$$\frac{7}{40000}m^{3}$$

Differentiate w.r.t. m

$$\frac{21m^{2}}{40000}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1.75\times \frac{1}{10000}m^{3})$$

Multiply 1.75 and \frac{1}{10000} to get \frac{7}{40000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{7}{40000}m^{3})$$

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

$$3\times \frac{7}{40000}m^{3-1}$$

Multiply 3 times \frac{7}{40000}.

$$\frac{21}{40000}m^{3-1}$$

Subtract 1 from 3.

$$\frac{21}{40000}m^{2}$$