Final answer to the problem
$e^x\left(1-\mathrm{tanh}\left(x\right)\right)\mathrm{sech}\left(x\right)$
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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
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=e^x$ and $g=\mathrm{sech}\left(x\right)$
$\frac{d}{dx}\left(e^x\right)\mathrm{sech}\left(x\right)+e^x\frac{d}{dx}\left(\mathrm{sech}\left(x\right)\right)$
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$\frac{d}{dx}\left(e^x\right)\mathrm{sech}\left(x\right)+e^x\frac{d}{dx}\left(\mathrm{sech}\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of e^xsech(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^x and g=\mathrm{sech}\left(x\right). Applying the derivative of the exponential function. Taking the derivative of hyperbolic secant. The derivative of the linear function is equal to 1.
Final answer to the problem
$e^x\left(1-\mathrm{tanh}\left(x\right)\right)\mathrm{sech}\left(x\right)$
