Dy is the differential of y, that is, the derivative of x in the formula containing y.
Dx is not the transformation quantity of X, but the variation quantity of X is Δ x, and Δ x and dx are two completely different concepts. δx is a nonlinear variable and dx is a linear variable, and their relationship will play an unparalleled role in engineering numerical analysis.
The y corresponding to dx is called dy, which is differential; Y corresponding to Δ x is called Δ y, which means variation. Generally speaking, the function y obtained by dimensional analysis is almost impossible to be a linear function, and in 99% cases, y is a nonlinear function.
Methods of extended data derivation:
(1) Steps to find the derivative of the function y=f(x) at x0:?
① Find the increment δ y = f (x0+δ x)-f (x0) of the function?
② Find the average change rate?
③ Seek the limit and derivative.
(2) Derivative formulas of several common functions:?
① C'=0(C is a constant);
②(x^n)'=nx^(n- 1)(n∈q)； ?
③(sinx)' = cosx； ?
④(cosx)' =-sinx； ?
⑤(e^x)'=e^x；
⑥ (a x)' = a A Xin (ln is natural logarithm)?
⑦ loga(x)'=( 1/x)loga(e)？
(3) Four algorithms of derivative:?
①(u v)'=u' v '
②(uv)'=u'v+uv '？
③(u/v)'=(u'v-uv')/ v^2？
④[u(v)]'=[u'(v)]*v' (u(v) is the compound function f[g(x)])?