Solve 4t^-6u^6/28t^9u^-9

$$\frac { 4 t ^ { - 6 } u ^ { 6 } } { 28 t ^ { 9 } u ^ { - 9 } }$$

Evaluate

$$\frac{\left(\frac{u}{t}\right)^{15}}{7}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{t^{-6}u^{6}}{7u^{-9}t^{9}}$$

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

$$\frac{t^{-6}u^{15}}{7t^{9}}$$

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

$$\frac{u^{15}}{7t^{15}}$$

Differentiate w.r.t. t

$$-\frac{15u^{15}}{7t^{16}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{4u^{6}u^{9}}{28}t^{-6-9})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{u^{15}}{7}t^{-15})$$

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}.

$$-15\times \frac{u^{15}}{7}t^{-15-1}$$

Do the arithmetic.

$$\left(-\frac{15u^{15}}{7}\right)t^{-16}$$