Final answer to the problem
$y^{\prime}=\frac{e^y+xe^y-\sin\left(y\right)}{1+x\cos\left(y\right)}$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Can't find a method? Tell us so we can add it.
1
Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
Learn how to solve problems step by step online.
$\frac{d}{dx}\left(y+x\sin\left(y\right)\right)=\frac{d}{dx}\left(xe^y\right)$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(y+xsin(y)=xe^y). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=e^y. The derivative of the linear function is equal to 1. Applying the derivative of the exponential function.
Final answer to the problem
$y^{\prime}=\frac{e^y+xe^y-\sin\left(y\right)}{1+x\cos\left(y\right)}$
