Solve b^4(1b^2)(12b^-8)

$$b ^ { 4 } ( 1 b ^ { 2 } ) ( 12 b ^ { - 8 } )$$

Evaluate

$$\frac{12}{b^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$b^{6}\times 1\times 12b^{-8}$$

To multiply powers of the same base, add their exponents. Add 6 and -8 to get -2.

$$b^{-2}\times 1\times 12$$

Multiply 1 and 12 to get 12.

$$b^{-2}\times 12$$

Differentiate w.r.t. b

$$-\frac{24}{b^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{6}\times 1\times 12b^{-8})$$

To multiply powers of the same base, add their exponents. Add 6 and -8 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-2}\times 1\times 12)$$

Multiply 1 and 12 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-2}\times 12)$$

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

$$-2\times 12b^{-2-1}$$

Multiply -2 times 12.

$$-24b^{-2-1}$$

Subtract 1 from -2.

$$-24b^{-3}$$