Exercise
$\frac{d}{dx}arctan\left(xy\right)=12ln\left(x^2+y^2\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(arctan(xy))=12ln(x^2+y^2). Taking the derivative of arctangent. The power of a product is equal to the product of it's factors raised to the same power. 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.
Find the implicit derivative d/dx(arctan(xy))=12ln(x^2+y^2)
Final answer to the exercise
$y^{\prime}=\frac{12\ln\left(x^2+y^2\right)+12x^2y^2\ln\left(x^2+y^2\right)-y}{x}$