Solve 0:a^8-b^3

$$0 : a ^ { 8 } - b ^ { 3 }$$

Evaluate

$$-b^{3}$$

Solution Steps

Zero divided by any non-zero term gives zero.

$$0-b^{3}$$

Anything plus zero gives itself.

$$-b^{3}$$

Differentiate w.r.t. b

$$-3b^{2}$$

Steps Using Definition of a Derivative

Zero divided by any non-zero term gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}b}(0-b^{3})$$

Anything plus zero gives itself.

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

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

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

Multiply 3 times -1.

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

Subtract 1 from 3.

$$-3b^{2}$$