Solve (-2)*B^-10*4*10^5

$$( - 2 ) \times B ^ { - 10 } \times 4 \times 10 ^ { 5 }$$

Evaluate

$$-\frac{800000}{B^{10}}$$

Solution Steps

Multiply -2 and 4 to get -8.

$$-8B^{-10}\times 10^{5}$$

Calculate 10 to the power of 5 and get 100000.

$$-8B^{-10}\times 100000$$

Multiply -8 and 100000 to get -800000.

$$-800000B^{-10}$$

Differentiate w.r.t. B

$$\frac{8000000}{B^{11}}$$

Steps Using Definition of a Derivative

Multiply -2 and 4 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}B}(-8B^{-10}\times 10^{5})$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\mathrm{d}}{\mathrm{d}B}(-8B^{-10}\times 100000)$$

Multiply -8 and 100000 to get -800000.

$$\frac{\mathrm{d}}{\mathrm{d}B}(-800000B^{-10})$$

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

$$-10\left(-800000\right)B^{-10-1}$$

Multiply -10 times -800000.

$$8000000B^{-10-1}$$

Subtract 1 from -10.

$$8000000B^{-11}$$