Exercise
$\frac{d}{dx}\left(x^{\frac{1}{2}}+y^{\frac{3}{4}}=-5y\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(x^(1/2)+y^(3/4)=-5y). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the implicit derivative d/dx(x^(1/2)+y^(3/4)=-5y)
Final answer to the exercise
$y^{\prime}=\frac{-2\sqrt[4]{y}}{\left(3+20\sqrt[4]{y}\right)\sqrt{x}}$