Solve -2(b)^-2*3(b^3)^2

$$- 2 ( b ) ^ { - 2 } \times 3 ( b ^ { 3 } ) ^ { 2 }$$

Evaluate

$$-6b^{4}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$-2b^{-2}\times 3b^{6}$$

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

$$-2b^{4}\times 3$$

Multiply -2 and 3 to get -6.

$$-6b^{4}$$

Differentiate w.r.t. b

$$-24b^{3}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-2b^{-2}\times 3b^{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(-2b^{4}\times 3)$$

Multiply -2 and 3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-6b^{4})$$

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

$$4\left(-6\right)b^{4-1}$$

Multiply 4 times -6.

$$-24b^{4-1}$$

Subtract 1 from 4.

$$-24b^{3}$$