Solve b^-4/b^-6

$$\frac { b ^ { - 4 } } { b ^ { - 6 } }$$

Differentiate w.r.t. b

$$2b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{-4-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2b^{2-1}$$

Do the arithmetic.

$$2b^{1}$$

For any term t, t^{1}=t.

$$2b$$

Evaluate

$$b^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -4 to get 2.

$$b^{2}$$