Final answer to the problem
$\frac{-e^x}{\sqrt{1-e^{2x}}}$
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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 arccosine
$\frac{-1}{\sqrt{1-\left(e^x\right)^2}}\frac{d}{dx}\left(e^x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{-1}{\sqrt{1-\left(e^x\right)^2}}\frac{d}{dx}\left(e^x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of arccos(e^x). Taking the derivative of arccosine. Simplify \left(e^x\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals 2. Applying the derivative of the exponential function. Multiply the fraction by the term .
Final answer to the problem
$\frac{-e^x}{\sqrt{1-e^{2x}}}$
