Calculus/calc ab

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Expert: - 9/30/2010


Question
how do I use the definition to take the derivative of 1/((x+3)^1/2 )?  

Answer
The definition says if f(x) = x^n, the derivative is
f'(x) = nx^(n-1).

For this case, we have x+3 instead of x and -1/2 in place of n.
The derivative of both x and x+3 is 1, so this is no worry.

To take the derivative of f(x) = (x+3)^(-1/2) gives
f'(x) = (-1/2)(x+3)^(-3/2).

Putting it back in proper form gives f'(x) = -1/[2(x+3)^(3/2)].




Note that if the x were replaced with a 2x, the chain rule would multiply the result by 2 since the derivative of 2x is 2.

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