Solve 3{x}^frac{2{3}}-5{x}^frac{1{3}}-12

$$3 { x }^{ \frac{ 2 }{ 3 } } -5 { x }^{ \frac{ 1 }{ 3 } } -12$$

Differentiate w.r.t. x

$$\frac{2}{\sqrt[3]{x}}-\frac{5}{3x^{\frac{2}{3}}}$$

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}.

$$\frac{2}{3}\times 3x^{\frac{2}{3}-1}+\frac{1}{3}\left(-5\right)x^{\frac{1}{3}-1}$$

Multiply \frac{2}{3} times 3.

$$2x^{\frac{2}{3}-1}+\frac{1}{3}\left(-5\right)x^{\frac{1}{3}-1}$$

Subtract 1 from \frac{2}{3}.

$$2x^{-\frac{1}{3}}+\frac{1}{3}\left(-5\right)x^{\frac{1}{3}-1}$$

Multiply \frac{1}{3} times -5.

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

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

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

Evaluate

$$3x^{\frac{2}{3}}-5\sqrt[3]{x}-12$$