Exercise
$\frac{d}{dx}\sqrt{x+y}=x^4+y^5$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx((x+y)^(1/2)=x^4+y^5). 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((x+y)^(1/2)=x^4+y^5)
Final answer to the exercise
$y^{\prime}=\frac{8x^{3}\sqrt{x+y}-1}{1-10y^{4}\sqrt{x+y}}$