Final answer to the problem
$\frac{1}{x\sqrt{\left(\frac{x}{a}\right)^2-1}}$
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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
$\frac{1}{\frac{x}{a}\sqrt{\left(\frac{x}{a}\right)^2-1}}\frac{d}{dx}\left(\frac{x}{a}\right)$
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$\frac{1}{\frac{x}{a}\sqrt{\left(\frac{x}{a}\right)^2-1}}\frac{d}{dx}\left(\frac{x}{a}\right)$
Learn how to solve problems step by step online. Find the derivative of arcsec(x/a). Taking the derivative of arcsecant. Divide fractions \frac{1}{\frac{x}{a}\sqrt{\left(\frac{x}{a}\right)^2-1}} 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 (\frac{1}{a}) is equal to the constant times the derivative of the function. Multiplying fractions \frac{a}{x\sqrt{\left(\frac{x}{a}\right)^2-1}} \times \frac{1}{a}.
Final answer to the problem
$\frac{1}{x\sqrt{\left(\frac{x}{a}\right)^2-1}}$
