Solve {l}{(7.1*10^8m)}{+(2.4*10^8m)}

$$\left. \begin{array} { l } { ( 7.1 \times 10 ^ { 8 } m ) } \\ { + ( 2.4 \times 10 ^ { 8 } m ) } \end{array} \right.$$

Evaluate

$$950000000m$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$7.1\times 100000000m+2.4\times 10^{8}m$$

Multiply 7.1 and 100000000 to get 710000000.

$$710000000m+2.4\times 10^{8}m$$

Calculate 10 to the power of 8 and get 100000000.

$$710000000m+2.4\times 100000000m$$

Multiply 2.4 and 100000000 to get 240000000.

$$710000000m+240000000m$$

Combine 710000000m and 240000000m to get 950000000m.

$$950000000m$$

Differentiate w.r.t. m

$$950000000$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(7.1\times 100000000m+2.4\times 10^{8}m)$$

Multiply 7.1 and 100000000 to get 710000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(710000000m+2.4\times 10^{8}m)$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(710000000m+2.4\times 100000000m)$$

Multiply 2.4 and 100000000 to get 240000000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(710000000m+240000000m)$$

Combine 710000000m and 240000000m to get 950000000m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(950000000m)$$

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

$$950000000m^{1-1}$$

Subtract 1 from 1.

$$950000000m^{0}$$

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

$$950000000\times 1$$

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

$$950000000$$