Solve (-b^3)*(4b^4)=

$$( - b ^ { 3 } ) \cdot ( 4 b ^ { 4 } ) =$$

Evaluate

$$-4b^{7}$$

Solution Steps

Multiply -1 and 4 to get -4.

$$-4b^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-4b^{7}$$

Differentiate w.r.t. b

$$-28b^{6}$$

Steps Using Definition of a Derivative

Multiply -1 and 4 to get -4.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-4b^{7})$$

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

$$7\left(-4\right)b^{7-1}$$

Multiply 7 times -4.

$$-28b^{7-1}$$

Subtract 1 from 7.

$$-28b^{6}$$