Solve x^frac{1{2}}-5x^frac{1{4}}+4

$$x ^ { \frac { 1 } { 2 } } - 5 x ^ { \frac { 1 } { 4 } } + 4$$

Differentiate w.r.t. x

$$\frac{1}{2\sqrt{x}}-\frac{5}{4x^{\frac{3}{4}}}$$

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}.

$$\frac{1}{2}x^{\frac{1}{2}-1}+\frac{1}{4}\left(-5\right)x^{\frac{1}{4}-1}$$

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

$$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{4}\left(-5\right)x^{\frac{1}{4}-1}$$

Multiply \frac{1}{4} times -5.

$$\frac{1}{2}x^{-\frac{1}{2}}-\frac{5}{4}x^{\frac{1}{4}-1}$$

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

$$\frac{1}{2}x^{-\frac{1}{2}}-\frac{5}{4}x^{-\frac{3}{4}}$$

Evaluate

$$\sqrt{x}-5\sqrt[4]{x}+4$$