Solve 3{x}^frac{2{3}}-4{x}^frac{1{2}}-2

$$3 { x }^{ \frac{ 2 }{ 3 } } -4 { x }^{ \frac{ 1 }{ 2 } } -2$$

Differentiate w.r.t. x

$$\frac{2\left(\sqrt[6]{x}-1\right)}{\sqrt{x}}$$

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}.

$$\frac{2}{3}\times 3x^{\frac{2}{3}-1}+\frac{1}{2}\left(-4\right)x^{\frac{1}{2}-1}$$

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

$$2x^{\frac{2}{3}-1}+\frac{1}{2}\left(-4\right)x^{\frac{1}{2}-1}$$

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

$$2x^{-\frac{1}{3}}+\frac{1}{2}\left(-4\right)x^{\frac{1}{2}-1}$$

Multiply \frac{1}{2} times -4.

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

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

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

Evaluate

$$3x^{\frac{2}{3}}-4\sqrt{x}-2$$