Solve 3,54*10^3m^3+3,4*10^6m^3

$$3,54 \times 10 ^ { 3 } m ^ { 3 } + 3,4 \times 10 ^ { 6 } m ^ { 3 }$$

Evaluate

$$3403540m^{3}$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$3,54\times 1000m^{3}+3,4\times 10^{6}m^{3}$$

Multiply 3,54 and 1000 to get 3540.

$$3540m^{3}+3,4\times 10^{6}m^{3}$$

Calculate 10 to the power of 6 and get 1000000.

$$3540m^{3}+3,4\times 1000000m^{3}$$

Multiply 3,4 and 1000000 to get 3400000.

$$3540m^{3}+3400000m^{3}$$

Combine 3540m^{3} and 3400000m^{3} to get 3403540m^{3}.

$$3403540m^{3}$$

Differentiate w.r.t. m

$$10210620m^{2}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3,54\times 1000m^{3}+3,4\times 10^{6}m^{3})$$

Multiply 3,54 and 1000 to get 3540.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3540m^{3}+3,4\times 10^{6}m^{3})$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3540m^{3}+3,4\times 1000000m^{3})$$

Multiply 3,4 and 1000000 to get 3400000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3540m^{3}+3400000m^{3})$$

Combine 3540m^{3} and 3400000m^{3} to get 3403540m^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3403540m^{3})$$

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

$$3\times 3403540m^{3-1}$$

Multiply 3 times 3403540.

$$10210620m^{3-1}$$

Subtract 1 from 3.

$$10210620m^{2}$$