Solve frac{5s^{7}t^8u}{5s^9t^9u^4}

$$\frac { 5 s ^ { 7 } t ^ { 8 } u } { 5 s ^ { 9 } t ^ { 9 } u ^ { 4 } }$$

Differentiate w.r.t. s

$$-\frac{2}{t\left(su\right)^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{5ut^{8}}{5u^{4}t^{9}}s^{7-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{1}{tu^{3}}s^{-2})$$

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}.

$$-2\times \frac{1}{tu^{3}}s^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{2}{tu^{3}}\right)s^{-3}$$

Evaluate

$$\frac{1}{ts^{2}u^{3}}$$

Solution Steps

Cancel out 5us^{7}t^{8} in both numerator and denominator.

$$\frac{1}{ts^{2}u^{3}}$$