Solve 2.2*10^4quad(b)quad9

$$2.2 \times 10 ^ { 4 } \quad ( b ) \quad 9$$

Evaluate

$$198000b$$

Solution Steps

Calculate 10 to the power of 4 and get 10000.

$$2.2\times 10000b\times 9$$

Multiply 2.2 and 10000 to get 22000.

$$22000b\times 9$$

Multiply 22000 and 9 to get 198000.

$$198000b$$

Differentiate w.r.t. b

$$198000$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 4 and get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2.2\times 10000b\times 9)$$

Multiply 2.2 and 10000 to get 22000.

$$\frac{\mathrm{d}}{\mathrm{d}b}(22000b\times 9)$$

Multiply 22000 and 9 to get 198000.

$$\frac{\mathrm{d}}{\mathrm{d}b}(198000b)$$

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

$$198000b^{1-1}$$

Subtract 1 from 1.

$$198000b^{0}$$

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

$$198000\times 1$$

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

$$198000$$