Exercise
$\frac{d}{dx}\left(2^{x^2}+2^{y^2}=2x^2y^2\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(2^x^2+2^y^2=2x^2y^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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(2^x^2+2^y^2=2x^2y^2)
Final answer to the exercise
$y^{\prime}=\frac{-\ln\left(2\right)\cdot 2^{\left(x^2+1\right)}x+4xy^2}{\left(\ln\left(2\right)2^{\left(y^2+1\right)}-4x^2\right)y}$