Final answer to the problem
$\frac{2}{x\sqrt{\frac{1}{4}x^{4}-1}}$
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Step-by-step Solution
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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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1
Taking the derivative of arcsecant
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$\frac{1}{\frac{1}{2}x^2\sqrt{\left(\frac{1}{2}x^2\right)^2-1}}\frac{d}{dx}\left(\frac{1}{2}x^2\right)$
Learn how to solve problems step by step online. Find the derivative of arcsec(1/2x^2). Taking the derivative of arcsecant. The power of a product is equal to the product of it's factors raised to the same power. Divide fractions \frac{1}{\frac{1}{2}x^2\sqrt{\frac{1}{4}x^{4}-1}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.
Final answer to the problem
$\frac{2}{x\sqrt{\frac{1}{4}x^{4}-1}}$
