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Exercise

$\frac{d}{dx}\left(x\sin\left(y\right)=xy^{-2}+\tan\left(xy\right)\right)$

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Final answer to the exercise

$\sin\left(y\right)+xy^{\prime}\cos\left(y\right)=\frac{1}{y^{2}}+x\frac{-2}{y^{3}}y^{\prime}+y\sec\left(xy\right)^2+xy^{\prime}\sec\left(xy\right)^2$

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  • Find the derivative using the definition
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  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
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  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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