Qn on Differentiation
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*10. Given that f(x) = sqrt[1 + sqrt(x)], where x is more than or equals to 0, show that f'(x) = 1/{4 sqrt[x + x sqrt(x)]}.
pls help me on this qn
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My strategy is I always convert to nice nice looking form then start doingOriginally posted by wishboy:*10. Given that f(x) = sqrt[1 + sqrt(x)], where x is more than or equals to 0, show that f'(x) = 1/{4 sqrt[x + x sqrt(x)]}.
pls help me on this qn
f(x) = (1 + x^0.5) ^ 0.5
so f'(x) = 0.5 * (1 + x^0.5)^(-0.5) * (d/dx {x^0.5} ) => chain rule I think
f'(x) = 0.5 * (1 + x^0.5)^(-0.5) * 0.5 * (x^-0.5)
f'(x) = 0.25 (x + x sqrt(x) ) ^ -0.5
f'(x) = 1/{4 sqrt[x + x sqrt(x)]} (shown) -
erm wad does f'(x) mean ar?
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means differentiate f(x), or rather, a more accurate description is the first differential of f(x)Originally posted by wishboy:erm wad does f'(x) mean ar? -
oh ok
y must they write until like so chim lol
can jus write differentiate the following w.r.t. x mah
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because it is a short formOriginally posted by wishboy:oh ok
y must they write until like so chim lol
can jus write differentiate the following w.r.t. x mah
and when you reach till higher differentials, it is an easier and shorter way of representing them
f''(x) is differentiate f(x) twice, etc
or the '' could be replaced by (3) or other numbers, which means 3rd differential or etc...
or
when you have many different types of function
f(x), g(x), h(x), etc
it is clearer and easier if you see differentials as
f'(x), g'(x), h'(x), etc... -
o...
i read ur post i alr confuse liao
so many functions
thanks for ur help ! -
erm... not impt de... just extra information...Originally posted by wishboy:o...
i read ur post i alr confuse liao
so many functions
For now, just take it as f'(x) is d/dx of f(x)
Slowly you will understand