Solve 1,0*10^-3*34m^3=

$$1,0 * 10 ^ { - 3 } \times 34 m ^ { 3 } =$$

Evaluate

$$\frac{17m^{3}}{500}$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$1\times \frac{1}{1000}\times 34m^{3}$$

Multiply 1 and \frac{1}{1000} to get \frac{1}{1000}.

$$\frac{1}{1000}\times 34m^{3}$$

Multiply \frac{1}{1000} and 34 to get \frac{17}{500}.

$$\frac{17}{500}m^{3}$$

Differentiate w.r.t. m

$$\frac{51m^{2}}{500}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1\times \frac{1}{1000}\times 34m^{3})$$

Multiply 1 and \frac{1}{1000} to get \frac{1}{1000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1000}\times 34m^{3})$$

Multiply \frac{1}{1000} and 34 to get \frac{17}{500}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{17}{500}m^{3})$$

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

$$3\times \frac{17}{500}m^{3-1}$$

Multiply 3 times \frac{17}{500}.

$$\frac{51}{500}m^{3-1}$$

Subtract 1 from 3.

$$\frac{51}{500}m^{2}$$