American Preparation H Wrap

Derivata del prodotto di funzioni

Here we begin to move on the complicated: If I
the product of two functions and I do want the derivative:
The first derivative of the second derivative is not over 'the first in that state for the second derivative of the symbols in

if y = f (x) · g (x)

then y' = f '(x) · g (x) + f (x) · g '(x)
example
the derivative of the function y =
x3senx
The derivative of x3 and' The derivative of 3x2
senx and 'cosx

then Y' = 3x2senx + x3cosx
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important consequences: if I make a constant for the derivative of a function will be enough 'multiply the constant for the derivative of the function demonstration

ie' I can extract the sign of the constants derived
example
y = 3x4 3
Since a constant multiplied by the derivative of x4
y '= 3 • 4 x3
y' = 12 x3
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If you need proof of the rule of the derivative of a product
----------------------------------- We do some exercises to
--------------------------------------------- fine tune the rule
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And if I do the derivative of a product of three or more 'functions?
Do not worry, the rule 'always the same, but adapted to more' functions, for example, if you do
derivative of the function y = f (x) · g (x) * h (x)

then y '= f '(x) · g (x) * h (x) + f (x) · g' (x) * h (x) + f (x) · g (x) * h '(x)
example:
the derivative of the function y = x5
· cosx · Log
The derivative of x and x5 '5x4
The derivative of cosx and' - senx
The derivative of log x '1 / x

then y' = 5x4 · cosx · Log x + x5 · (- senx) · log x + x5 · cosx • 1 / x
ie '
y' = 5x4·cosx ·log x - x5·senx ·log x + x5·cosx · 1/x