Solve u(3/9)^2-sqrt{frac{16/81}}{sqrt{1/36}}

$$u \frac { ( \frac { 3 } { 9 } ) ^ { 2 } - \sqrt { \frac { 16 } { 81 } } } { \sqrt { \frac { 1 } { 36 } } }$$

Evaluate

$$-\frac{\sqrt{36}u}{3}$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$u\times \frac{\left(\frac{1}{3}\right)^{2}-\sqrt{\frac{16}{81}}}{\sqrt{\frac{1}{36}}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$u\times \frac{\frac{1}{9}-\sqrt{\frac{16}{81}}}{\sqrt{\frac{1}{36}}}$$

Rewrite the square root of the division \frac{16}{81} as the division of square roots \frac{\sqrt{16}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$u\times \frac{\frac{1}{9}-\frac{4}{9}}{\sqrt{\frac{1}{36}}}$$

Subtract \frac{4}{9} from \frac{1}{9} to get -\frac{1}{3}.

$$u\times \frac{-\frac{1}{3}}{\sqrt{\frac{1}{36}}}$$

Rewrite the square root of the division \frac{1}{36} as the division of square roots \frac{\sqrt{1}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$u\times \frac{-\frac{1}{3}}{\frac{1}{6}}$$

Divide -\frac{1}{3} by \frac{1}{6} by multiplying -\frac{1}{3} by the reciprocal of \frac{1}{6}.

$$u\left(-\frac{1}{3}\right)\times 6$$

Multiply -\frac{1}{3} and 6 to get -2.

$$u\left(-2\right)$$

Differentiate w.r.t. u

$$-\frac{\sqrt{36}}{3} = -2$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\times \frac{\left(\frac{1}{3}\right)^{2}-\sqrt{\frac{16}{81}}}{\sqrt{\frac{1}{36}}})$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\times \frac{\frac{1}{9}-\sqrt{\frac{16}{81}}}{\sqrt{\frac{1}{36}}})$$

Rewrite the square root of the division \frac{16}{81} as the division of square roots \frac{\sqrt{16}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\times \frac{\frac{1}{9}-\frac{4}{9}}{\sqrt{\frac{1}{36}}})$$

Subtract \frac{4}{9} from \frac{1}{9} to get -\frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\times \frac{-\frac{1}{3}}{\sqrt{\frac{1}{36}}})$$

Rewrite the square root of the division \frac{1}{36} as the division of square roots \frac{\sqrt{1}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\times \frac{-\frac{1}{3}}{\frac{1}{6}})$$

Divide -\frac{1}{3} by \frac{1}{6} by multiplying -\frac{1}{3} by the reciprocal of \frac{1}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\left(-\frac{1}{3}\right)\times 6)$$

Multiply -\frac{1}{3} and 6 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u\left(-2\right))$$

The derivative of ax^{n} is nax^{n-1}.

$$-2u^{1-1}$$

Subtract 1 from 1.

$$-2u^{0}$$

For any term t except 0, t^{0}=1.

$$-2$$