Solve 6asqrt{a/18}-3a^2sqrt{2/a}

$$6 a \sqrt { \frac { a } { 18 } } - 3 a ^ { 2 } \sqrt { \frac { 2 } { a } }$$

Differentiate w.r.t. a

$$-3\sqrt{2a}$$

Steps Using Derivative Rule for Sum

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}.

$$6\sqrt{\frac{a}{18}}a^{1-1}+2\left(-3\sqrt{\frac{2}{a}}\right)a^{2-1}$$

Subtract 1 from 1.

$$\sqrt{2a}a^{0}+2\left(-3\sqrt{\frac{2}{a}}\right)a^{2-1}$$

Multiply 2 times -3\sqrt{2a^{-1}}.

$$\sqrt{2a}a^{0}+\left(-\frac{12}{\sqrt{2a}}\right)a^{2-1}$$

Subtract 1 from 2.

$$\sqrt{2a}a^{0}+\left(-\frac{12}{\sqrt{2a}}\right)a^{1}$$

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

$$\sqrt{2a}a^{0}+\left(-\frac{12}{\sqrt{2a}}\right)a$$

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

$$\sqrt{2a}\times 1+\left(-\frac{12}{\sqrt{2a}}\right)a$$

For any term t, t\times 1=t and 1t=t.

$$\sqrt{2a}+\left(-\frac{12}{\sqrt{2a}}\right)a$$

Evaluate

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