Final answer to the problem
$\frac{\mathrm{arccot}\left(x\right)-\arctan\left(x\right)}{1+x^2}$
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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
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\arctan\left(x\right)$ and $g=\mathrm{arccot}\left(x\right)$
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$\frac{d}{dx}\left(\arctan\left(x\right)\right)\mathrm{arccot}\left(x\right)+\frac{d}{dx}\left(\mathrm{arccot}\left(x\right)\right)\arctan\left(x\right)$
Learn how to solve problems step by step online. Find the derivative of arctan(x)arccot(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\arctan\left(x\right) and g=\mathrm{arccot}\left(x\right). Taking the derivative of arctangent. The derivative of the linear function is equal to 1. Multiply the fraction by the term .
Final answer to the problem
$\frac{\mathrm{arccot}\left(x\right)-\arctan\left(x\right)}{1+x^2}$
