Solve 78*82quad(b)(998)^2

$$78 \times 82 \quad ( b ) ( 998 ) ^ { 2 }$$

Evaluate

$$6370441584b$$

Solution Steps

Multiply 78 and 82 to get 6396.

$$6396b\times 998^{2}$$

Calculate 998 to the power of 2 and get 996004.

$$6396b\times 996004$$

Multiply 6396 and 996004 to get 6370441584.

$$6370441584b$$

Differentiate w.r.t. b

$$6370441584$$

Steps Using Definition of a Derivative

Multiply 78 and 82 to get 6396.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6396b\times 998^{2})$$

Calculate 998 to the power of 2 and get 996004.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6396b\times 996004)$$

Multiply 6396 and 996004 to get 6370441584.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6370441584b)$$

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

$$6370441584b^{1-1}$$

Subtract 1 from 1.

$$6370441584b^{0}$$

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

$$6370441584\times 1$$

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

$$6370441584$$