Solving: $\frac{d}{dx}\left(6\sqrt{y}=x-1\right)$
Exercise
$\frac{dy}{dx}\left(6\sqrt{y}=x-1\right)$
Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the implicit derivative d/dx(6y^(1/2)=x-1). 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply the fraction and term in 6\cdot \left(\frac{1}{2}\right)y^{-\frac{1}{2}}\frac{d}{dx}\left(y\right).
Find the implicit derivative d/dx(6y^(1/2)=x-1)
Final answer to the exercise
$y^{\prime}=\frac{\sqrt{y}}{3}$