What is the derivative of \sqrt[4]{5/4 x} ?

The derivative of \sqrt[4]{5/4 x} is (5^{1/4})/(4sqrt(2)x^{3/4)}

What is the first derivative of \sqrt[4]{5/4 x} ?

The first derivative of \sqrt[4]{5/4 x} is (5^{1/4})/(4sqrt(2)x^{3/4)}

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

Solution steps

Apply the chain rule:

\frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{5}{4} x)

= \frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{5}{4} x)

\frac{d}{d x} (\frac{5}{4} x) = \frac{5}{4}

= \frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \cdot \frac{5}{4}

Simplify

\frac{1}{4 ( \frac{5}{4} x ) ^{\frac{3}{4}}} \cdot \frac{5}{4} : \frac{5 ^{\frac{1}{4}}}{4 2 x ^{\frac{3}{4}}}

= \frac{5 ^{\frac{1}{4}}}{4 2 x ^{\frac{3}{4}}}

\int \frac{1}{x ^{2} - 2 x + 26} d x

x^{^{''}} - a x = 0

x \to 0 lim (x^{2} cos (\frac{8}{x}))

y = \frac{3 x - 2}{x}

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} + x + 1})

What is the derivative of \sqrt[4]{5/4 x} ?
The derivative of \sqrt[4]{5/4 x} is (5^{1/4})/(4sqrt(2)x^{3/4)}
What is the first derivative of \sqrt[4]{5/4 x} ?
The first derivative of \sqrt[4]{5/4 x} is (5^{1/4})/(4sqrt(2)x^{3/4)}