Final answer to the problem
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
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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=y$
The derivative of the linear function is equal to $1$
Applying the derivative of the exponential function
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=y$
The derivative of the linear function is equal to $1$
Multiply both sides of the equation by $xy$
Group the terms of the equation by moving the terms that have the variable $y^{\prime}$ to the left side, and those that do not have it to the right side
Move everything to the left hand side of the equation
Factoring by $y+xy^{\prime}$
Break the equation in $2$ factors and set each factor equal to zero, to obtain simpler equations
Solve the equation ($1$)
We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $y$ from both sides of the equation
Divide both sides of the equation by $x$
Solve the equation ($2$)
This equation $-e^{xy}xy+1=0$ has no solutions in the real plane
The solution of the equation is