Exercise
$\frac{d}{dx}\left(sen\left(y-x^2\right)-ln\left(y-x^2\right)+2\sqrt{\left(y-x^2\right)}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative d/dx(sin(y-x^2)-ln(y-x^2)2(y-x^2)^(1/2)) using the sum rule. 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. 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 2\cdot \left(\frac{1}{2}\right)\left(y-x^2\right)^{-\frac{1}{2}}\frac{d}{dx}\left(y-x^2\right).
Find the derivative d/dx(sin(y-x^2)-ln(y-x^2)2(y-x^2)^(1/2)) using the sum rule
Final answer to the exercise
$-2x\cos\left(y-x^2\right)+\frac{2x}{y-x^2}+\frac{-2x}{\sqrt{y-x^2}}$