Solve 4q^-1r^2/10q^3r

$$\frac { 4 q ^ { - 1 } r ^ { 2 } } { 10 q ^ { 3 } r }$$

Evaluate

$$\frac{2r}{5q^{4}}$$

Solution Steps

Cancel out 2r in both numerator and denominator.

$$\frac{2\times \frac{1}{q}r}{5q^{3}}$$

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

$$\frac{2r}{5q^{4}}$$

Differentiate w.r.t. q

$$-\frac{8r}{5q^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{4r^{2}}{10r}q^{-1-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{2r}{5}q^{-4})$$

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}.

$$-4\times \frac{2r}{5}q^{-4-1}$$

Do the arithmetic.

$$\left(-\frac{8r}{5}\right)q^{-5}$$