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

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

Differentiate w.r.t. x

$$-\frac{1}{\sqrt{x}}+\frac{1}{4x^{\frac{3}{4}}}$$

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}.

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

Subtract 1 from \frac{1}{4}.

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

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

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

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

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

Evaluate

$$-2\sqrt{x}+\sqrt[4]{x}+1$$