Final answer to the problem
$\frac{x\mathrm{tanh}\left(\sqrt{x^2+4}\right)}{\sqrt{x^2+4}\mathrm{sech}\left(\sqrt{x^2+4}\right)}$
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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
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$-\mathrm{sech}\left(\sqrt{x^2+4}\right)^{-2}\frac{d}{dx}\left(\mathrm{sech}\left(\sqrt{x^2+4}\right)\right)$
Learn how to solve problems step by step online. Find the derivative of sech((x^2+4)^(1/2))^(-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}. Taking the derivative of hyperbolic secant. Any expression multiplied by 1 is equal to itself. When multiplying exponents with same base you can add the exponents: \mathrm{sech}\left(\sqrt{x^2+4}\right)^{-2}\frac{d}{dx}\left(\sqrt{x^2+4}\right)\mathrm{sech}\left(\sqrt{x^2+4}\right)\mathrm{tanh}\left(\sqrt{x^2+4}\right).
Final answer to the problem
$\frac{x\mathrm{tanh}\left(\sqrt{x^2+4}\right)}{\sqrt{x^2+4}\mathrm{sech}\left(\sqrt{x^2+4}\right)}$
