Homework SourseFind the differential of fx 1sqrt x3 1Solution ddxfx ddx1
Find the differential of f(x) = 1/sqrt x^3 + 1
Solution
d/dx(f(x)) = d/dx(1/sqrt(x^3)+1) | The derivative of f(x) is f\'(x): = | f\'(x) = d/dx(1/sqrt(x^3)+1) | Differentiate the sum term by term: = | f\'(x) = d/dx(1/sqrt(x^3))+d/dx(1) | The derivative of 1 is zero: = | f\'(x) = d/dx(1/sqrt(x^3))+0 | Use the chain rule, d/dx(1/sqrt(x^3)) = d/( du)1/sqrt(u) ( du)/( dx), where u = x^3 and d/( du)1/sqrt(u) = -1/(2 u^(3/2)): = | f\'(x) = -(d/dx(x^3))/(2 (x^3)^(3/2)) | The derivative of x^3 is 3 x^2: = | f\'(x) = -(3 x^2)/(2 (x^3)^(3/2))
