Solve 178kg/89*10^3kg/m^3*2*10^-6m^2

$$\frac { 178 kg } { 89 \times 10 ^ { 3 } kg / m ^ { 3 } \times 2 \times 10 ^ { - 6 } m ^ { 2 } }$$

Evaluate

$$1000m$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{178kg}{\frac{89\times 1000kg}{m^{3}}\times 2\times 10^{-6}m^{2}}$$

Multiply 89 and 1000 to get 89000.

$$\frac{178kg}{\frac{89000kg}{m^{3}}\times 2\times 10^{-6}m^{2}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{178kg}{\frac{89000kg}{m^{3}}\times 2\times \frac{1}{1000000}m^{2}}$$

Multiply 2 and \frac{1}{1000000} to get \frac{1}{500000}.

$$\frac{178kg}{\frac{89000kg}{m^{3}}\times \frac{1}{500000}m^{2}}$$

Multiply \frac{89000kg}{m^{3}} times \frac{1}{500000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{178kg}{\frac{89000kg}{m^{3}\times 500000}m^{2}}$$

Cancel out 1000 in both numerator and denominator.

$$\frac{178kg}{\frac{89gk}{500m^{3}}m^{2}}$$

Express \frac{89gk}{500m^{3}}m^{2} as a single fraction.

$$\frac{178kg}{\frac{89gkm^{2}}{500m^{3}}}$$

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

$$\frac{178kg}{\frac{89gk}{500m}}$$

Divide 178kg by \frac{89gk}{500m} by multiplying 178kg by the reciprocal of \frac{89gk}{500m}.

$$\frac{178kg\times 500m}{89gk}$$

Cancel out 89gk in both numerator and denominator.

$$2\times 500m$$

Multiply 2 and 500 to get 1000.

$$1000m$$

Differentiate w.r.t. m

$$1000$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89\times 1000kg}{m^{3}}\times 2\times 10^{-6}m^{2}})$$

Multiply 89 and 1000 to get 89000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89000kg}{m^{3}}\times 2\times 10^{-6}m^{2}})$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89000kg}{m^{3}}\times 2\times \frac{1}{1000000}m^{2}})$$

Multiply 2 and \frac{1}{1000000} to get \frac{1}{500000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89000kg}{m^{3}}\times \frac{1}{500000}m^{2}})$$

Multiply \frac{89000kg}{m^{3}} times \frac{1}{500000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89000kg}{m^{3}\times 500000}m^{2}})$$

Cancel out 1000 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89gk}{500m^{3}}m^{2}})$$

Express \frac{89gk}{500m^{3}}m^{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89gkm^{2}}{500m^{3}}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg}{\frac{89gk}{500m}})$$

Divide 178kg by \frac{89gk}{500m} by multiplying 178kg by the reciprocal of \frac{89gk}{500m}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{178kg\times 500m}{89gk})$$

Cancel out 89gk in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2\times 500m)$$

Multiply 2 and 500 to get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1000m)$$

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

$$1000m^{1-1}$$

Subtract 1 from 1.

$$1000m^{0}$$

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

$$1000\times 1$$

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

$$1000$$