Solve 1.3m01*6.02*10^23

$$1.3 m 01 \cdot 6.02 \cdot 10 ^ { 23 }$$

Evaluate

$$782600000000000000000000m_{0}$$

Solution Steps

Multiply 1.3 and 1 to get 1.3.

$$1.3m_{0}\times 6.02\times 10^{23}$$

Multiply 1.3 and 6.02 to get 7.826.

$$7.826m_{0}\times 10^{23}$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$7.826m_{0}\times 100000000000000000000000$$

Multiply 7.826 and 100000000000000000000000 to get 782600000000000000000000.

$$782600000000000000000000m_{0}$$

Differentiate w.r.t. m_0

$$782600000000000000000000$$

Steps Using Definition of a Derivative

Multiply 1.3 and 1 to get 1.3.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(1.3m_{0}\times 6.02\times 10^{23})$$

Multiply 1.3 and 6.02 to get 7.826.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(7.826m_{0}\times 10^{23})$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(7.826m_{0}\times 100000000000000000000000)$$

Multiply 7.826 and 100000000000000000000000 to get 782600000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(782600000000000000000000m_{0})$$

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

$$782600000000000000000000m_{0}^{1-1}$$

Subtract 1 from 1.

$$782600000000000000000000m_{0}^{0}$$

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

$$782600000000000000000000\times 1$$

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

$$782600000000000000000000$$