Solve 2ba^0/-4ba^-4

$$\frac { 2 b a ^ { 0 } } { - 4 b a ^ { - 4 } }$$

Evaluate

$$-\frac{a^{4}}{2}$$

Solution Steps

Cancel out 2b in both numerator and denominator.

$$\frac{a^{0}}{-2a^{-4}}$$

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

$$\frac{a^{4}}{-2}$$

Differentiate w.r.t. a

$$-2a^{3}$$

Steps Using Definition of a Derivative

Cancel out 2b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{0}}{-2a^{-4}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}}{-2})$$

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

$$4\left(-\frac{1}{2}\right)a^{4-1}$$

Multiply 4 times -\frac{1}{2}.

$$-2a^{4-1}$$

Subtract 1 from 4.

$$-2a^{3}$$