Solve 2{x}^frac{5{4}}+6{x}^frac{1{4}}+3x^-4

$$2 { x }^{ \frac{ 5 }{ 4 } } +6 { x }^{ \frac{ 1 }{ 4 } } +3 { x }^{ -4 }$$

Differentiate w.r.t. x

$$\frac{5\sqrt[4]{x}}{2}+\frac{3}{2x^{\frac{3}{4}}}-\frac{12}{x^{5}}$$

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}.

$$\frac{5}{4}\times 2x^{\frac{5}{4}-1}+\frac{1}{4}\times 6x^{\frac{1}{4}-1}-4\times 3x^{-4-1}$$

Multiply \frac{5}{4} times 2.

$$\frac{5}{2}x^{\frac{5}{4}-1}+\frac{1}{4}\times 6x^{\frac{1}{4}-1}-4\times 3x^{-4-1}$$

Subtract 1 from \frac{5}{4}.

$$\frac{5}{2}\sqrt[4]{x}+\frac{1}{4}\times 6x^{\frac{1}{4}-1}-4\times 3x^{-4-1}$$

Multiply \frac{1}{4} times 6.

$$\frac{5}{2}\sqrt[4]{x}+\frac{3}{2}x^{\frac{1}{4}-1}-4\times 3x^{-4-1}$$

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

$$\frac{5}{2}\sqrt[4]{x}+\frac{3}{2}x^{-\frac{3}{4}}-4\times 3x^{-4-1}$$

Multiply \frac{1}{4} times 6.

$$\frac{5}{2}\sqrt[4]{x}+\frac{3}{2}x^{-\frac{3}{4}}-12x^{-4-1}$$

Subtract 1 from -4.

$$\frac{5}{2}\sqrt[4]{x}+\frac{3}{2}x^{-\frac{3}{4}}-12x^{-5}$$

Evaluate

$$2x^{\frac{5}{4}}+6\sqrt[4]{x}+\frac{3}{x^{4}}$$