Exercise
$\frac{d}{dx}\left(x^2\:\cdot\:y^2\:=\:b\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(x^2y^2=b). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (b) is equal to zero. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^2 and g=y^2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Find the implicit derivative d/dx(x^2y^2=b)
Final answer to the exercise
$y^{\prime}=\frac{-y}{x}$