Final answer to the problem
$\frac{1}{2\left(1+x\right)\sqrt{2x+1}}$
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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 arctangent
$\frac{1}{1+\left(\sqrt{2x+1}\right)^2}\frac{d}{dx}\left(\sqrt{2x+1}\right)$
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$\frac{1}{1+\left(\sqrt{2x+1}\right)^2}\frac{d}{dx}\left(\sqrt{2x+1}\right)$
Learn how to solve problems step by step online. Find the derivative of arctan((2x+1)^(1/2)). Taking the derivative of arctangent. Cancel exponents \frac{1}{2} and 2. Add the values 1 and 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final answer to the problem
$\frac{1}{2\left(1+x\right)\sqrt{2x+1}}$
