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Can a general derivative of df(x) / dg(x) be computed, or is the denominator always strictly a sole variable?
For example, dx/d(x+5)
Can this be solved?
For another example, d(x^2)/d(x-4)
2 Answers
- 6 years ago
Since the differential of the constant is 0, dx/d(x+5) = dx/dx = 1. If x = f(t) and y = g(t), dy/dx = g'(t)/f'(t). For example, if x = cos(t) and y = sin(t) dy/dx = cos(t)/(-sin(t)) = - cotan(t). Note for the SECOND derivation the rule must be rewritten as d2y/dx2 = d/dx(dy/dx), and in our case d2y/dx2 = d/dt(-cotan(t))/d/dt(cos(t)) = -1/sin^3(t).