Solve -3b*4b^3*2b=

$$- 3 b \cdot 4 b ^ { 3 } \cdot 2 b =$$

Evaluate

$$-24b^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-3b^{5}\times 4\times 2$$

Multiply -3 and 4 to get -12.

$$-12b^{5}\times 2$$

Multiply -12 and 2 to get -24.

$$-24b^{5}$$

Differentiate w.r.t. b

$$-120b^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-3b^{5}\times 4\times 2)$$

Multiply -3 and 4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-12b^{5}\times 2)$$

Multiply -12 and 2 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-24b^{5})$$

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

$$5\left(-24\right)b^{5-1}$$

Multiply 5 times -24.

$$-120b^{5-1}$$

Subtract 1 from 5.

$$-120b^{4}$$