How do you differentiate a function that is in the form of f(g(x))? Meaning, what is the derivative of f(g(x))?
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use the chain rule :D
f(g(x))
d/dx f(g(x))
= f'(g(x)) * d/dx g(x)
= f'(g(x)) * g'(x)
For example:
y = √(x^2 + 5x + 1)
you take the derviative of the entire √ function as a whole, and multiply that by the derivative of the insdie of the fucntion.
y' = (1/2)(x^2 + 5x + 1)^(-1/2) * (2x + 5)
y' = (2x + 5) / (2√(x^2 + 5x + 1))
Or it could even be:
y = (x^2 + 1)^2
Take the deriavtive of the ^2 as a whole.
y' = 2(x^2 + 1) * (2x)
Hope this helps :D
f(g(x))
d/dx f(g(x))
= f'(g(x)) * d/dx g(x)
= f'(g(x)) * g'(x)
For example:
y = √(x^2 + 5x + 1)
you take the derviative of the entire √ function as a whole, and multiply that by the derivative of the insdie of the fucntion.
y' = (1/2)(x^2 + 5x + 1)^(-1/2) * (2x + 5)
y' = (2x + 5) / (2√(x^2 + 5x + 1))
Or it could even be:
y = (x^2 + 1)^2
Take the deriavtive of the ^2 as a whole.
y' = 2(x^2 + 1) * (2x)
Hope this helps :D
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f ' [g[x] ] g'[x]