What is the derivative of \sqrt[4]{(x^2+1/(x^2-1)}) ?

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

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

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

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- \frac{x}{( x ^{2} + 1 ) ^{\frac{3}{4}} ( x ^{2} - 1 ) ^{\frac{5}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( \frac{x ^{2} + 1}{x ^{2} - 1} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

= \frac{1}{4 ( \frac{x ^{2} + 1}{x ^{2} - 1} ) ^{\frac{3}{4}}} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1}) = - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

= \frac{1}{4 ( \frac{x ^{2} + 1}{x ^{2} - 1} ) ^{\frac{3}{4}}} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Simplify

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

= - \frac{x}{( x ^{2} + 1 ) ^{\frac{3}{4}} ( x ^{2} - 1 ) ^{\frac{5}{4}}}

12 x^{11} y + x^{12} y^{^{'}} = - 7 sec^{2} (x) \cdot tan (x)

\frac{d}{d x} ((2 x - e^{2} x)^{s i n (2 x)})

\int \frac{x}{t ^{2}} d t

4 x - 8

\frac{d}{d s} (\frac{s}{s ^{2} + 1})

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