Solve (-12a^5b^4/4a^5b)

$$( \frac { - 12 a ^ { 5 } b ^ { 4 } } { 4 a ^ { 5 } b } )$$

Evaluate

$$-3b^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-12\right)^{1}a^{5}b^{4}}{4^{1}a^{5}b^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(-12\right)^{1}}{4^{1}}a^{5-5}b^{4-1}$$

Subtract 5 from 5.

$$\frac{\left(-12\right)^{1}}{4^{1}}a^{0}b^{4-1}$$

For any number a except 0, a^{0}=1.

$$\frac{\left(-12\right)^{1}}{4^{1}}b^{4-1}$$

Subtract 1 from 4.

$$\frac{\left(-12\right)^{1}}{4^{1}}b^{3}$$

Divide -12 by 4.

$$-3b^{3}$$

Differentiate w.r.t. b

$$-9b^{2}$$

Steps Using Definition of a Derivative

Cancel out 4ba^{5} in both numerator and denominator.

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

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

$$3\left(-3\right)b^{3-1}$$

Multiply 3 times -3.

$$-9b^{3-1}$$

Subtract 1 from 3.

$$-9b^{2}$$