Solve 5b^3/azb

$$\frac { 5 b ^ { 3 } } { a z b }$$

Differentiate w.r.t. b

$$\frac{10b}{az}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5}{az}b^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5}{az}b^{2})$$

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}.

$$2\times \frac{5}{az}b^{2-1}$$

Do the arithmetic.

$$\frac{10}{az}b^{1}$$

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

$$\frac{10}{az}b$$

Evaluate

$$\frac{5b^{2}}{az}$$

Solution Steps

Cancel out b in both numerator and denominator.

$$\frac{5b^{2}}{az}$$