Exercise
$\frac{d}{dx}5y-x^2=\sqrt{x-y^3}$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(5y-x^2=(x-y^3)^(1/2)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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(5y-x^2=(x-y^3)^(1/2))
Final answer to the exercise
$y^{\prime}=\frac{4x\sqrt{x-y^3}+1}{10\sqrt{x-y^3}+3y^2}$