Exercise
$\frac{d}{dx}\left(tan^{-1}\left(3x^2y\right)=x+5xy^2\right)$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the implicit derivative d/dx(arctan(3x^2y)=x+5xy^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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 and g=y^2.
Find the implicit derivative d/dx(arctan(3x^2y)=x+5xy^2)
Final answer to the exercise
$y^{\prime}=\frac{6xy-90x^{5}y^{\left(3+{\prime}\right)}-1-9x^{4}y^2-5y^2-45x^{4}y^{4}}{\left(-3x+10y\right)x}$