Solve 3{x}^frac{2{5}}+6x+2

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

Differentiate w.r.t. x

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

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}.

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

Multiply \frac{2}{5} times 3.

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

Subtract 1 from \frac{2}{5}.

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

Subtract 1 from 1.

$$\frac{6}{5}x^{-\frac{3}{5}}+6x^{0}$$

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

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

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

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

Evaluate

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