Find the derivative of y with respect to x ylnx245sqrt3xSolu

Solution

y=ln((x^2+4)^5/sqrt(3-x)) dy/dx = 1/(x^2+4)^5/sqrt(3-x) * d/dx[(x^2+4)^5/sqrt(3-x)] dy/dx = 1/(x^2+4)^5/sqrt(3-x) * [sqrt(3-x)*10x(x^2+4)^4 - (x^2+4)^5*(-1/2sqrt(3-x)]/(3-x) dy/dx = sqrt(3-x)/(x^2+4)^5 * [20x(3-x)(x^2+4)^4 + (x^2+4)^5]/(3-x)^3/2 dy/dx = [20x(3-x) + x^2+4]/(3-x) dy/dx = [60x -20x^2 + x^2 + 4]/(3-x) dy/dx = [19x^2 - 60x - 4]/(x-3)