The derivation process of F (x) = x ^ 3 (x-3)

The derivation process of F (x) = x ^ 3 (x-3)

f(x)=x^3(x-3)=x^4-3x^3
f'(x)=4x^3-9x^2
Or F '(x) = (x ^ 3)' * (x-3) + (x-3) '* x ^ 3
=3x^2(x-3)+x^3
=4x^3-9x^2

In the implicit function derivation method, ellipse (X & # 178 / 16) + (Y & # 178 / 9) = 0, how to get (2x / 16) + (2yy '/ 9) = 0?
Y & # 178; the derivation is 2yy 'instead of 2Y? Solution

Here, y is understood as a composite function y = y (x)
Using the derivative method of compound function, f (U) '= f' * u '
That is to say, the derivative of Y ^ 2 to X is 2yy '

Who can tell me about the derivation of implicit function? I can't understand the derivation of X

The three key points are: 1. Y is a function of X, which should be treated according to the formula of compound function derivation. That is to say, it is multiplied by the derivative of Y. for example, y ^ 2 = x, two sides of X get 2yy '= 1, for example, LNY = x, two sides of X get y' / y = 12. When one variable in the product formula and quotient formula is derived, other variables are treated as constants. For example, e ^ y + xy-e = 0, two sides of X get e ^