Final answer to the problem
$\frac{e^{xy^3}y^3}{1+e^{2xy^3}}$
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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
Learn how to solve inverse trigonometric functions differentiation problems step by step online.
$\frac{1}{1+\left(e^{xy^3}\right)^2}\frac{d}{dx}\left(e^{xy^3}\right)$
Learn how to solve inverse trigonometric functions differentiation problems step by step online. Find the derivative of arctan(e^(xy^3)). Taking the derivative of arctangent. Simplify \left(e^{xy^3}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals xy^3 and n equals 2. Applying the derivative of the exponential function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.
Final answer to the problem
$\frac{e^{xy^3}y^3}{1+e^{2xy^3}}$
