Solve partial/b1/partialb=

$$\frac { \partial } { b } \frac { 1 } { \partial b } =$$

Evaluate

$$\frac{1}{b^{2}}$$

Solution Steps

Multiply \frac{∂}{b} times \frac{1}{∂b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{∂}{b∂b}$$

Cancel out ∂ in both numerator and denominator.

$$\frac{1}{bb}$$

Multiply b and b to get b^{2}.

$$\frac{1}{b^{2}}$$

Differentiate w.r.t. b

$$-\frac{2}{b^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{∂}{∂}b^{-1-1})$$

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.

$$-2b^{-3}$$