Solve x^1/3+6x^1/6+9

$$x ^ { 1 / 3 } + 6 x ^ { 1 / 6 } + 9$$

Differentiate w.r.t. x

$$\frac{1}{3x^{\frac{2}{3}}}+\frac{1}{x^{\frac{5}{6}}}$$

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}.

$$\frac{1}{3}x^{\frac{1}{3}-1}+\frac{1}{6}\times 6x^{\frac{1}{6}-1}$$

Subtract 1 from \frac{1}{3}.

$$\frac{1}{3}x^{-\frac{2}{3}}+\frac{1}{6}\times 6x^{\frac{1}{6}-1}$$

Multiply \frac{1}{6} times 6.

$$\frac{1}{3}x^{-\frac{2}{3}}+x^{\frac{1}{6}-1}$$

Subtract 1 from \frac{1}{6}.

$$\frac{1}{3}x^{-\frac{2}{3}}+x^{-\frac{5}{6}}$$

Evaluate

$$\left(\sqrt[6]{x}+3\right)^{2}$$