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Use the rules of differentiation to find the derivatives of the following function. Simplify terms wherever possible, but it is not necessary to factorise and then cancel any of the expressions.

2007-08-15 21:42:38 · 4 answers · asked by vanisha j 1 in Science & Mathematics Mathematics

4 answers

h(x) = 8 / (3√(5x^2 - 2x))
There are two ways to do this. Slightly simpler is first to rewrite h(x) as
h(x) = (8/3) (5x^2 - 2x)^(-1/2)
Then chain rule + power rule says
h'(x) = (8/3) (-1/2) (5x^2 - 2x)^(-3/2) [d/dx (5x^2 - 2x)]
= (8/3) (-1/2) (5x^2 - 2x)^(-3/2) [10x - 2]
= (-8/3) (5x^2 - 2x)^(-3/2) (5x - 1)

Alternatively, we can use the quotient rule and chain rule directly to get
h(x) = 8 / (3√(5x^2 - 2x))
h'(x) = {0 - 8(3) (1/2) (5x^2 - 2x)^(-1/2) [d/dx (5x^2 - 2x)]} / {(3√(5x^2 - 2x))^2}
= {-12 (5x^2 - 2x)^(-1/2) (10x - 2)} / {9 (5x^2 - 2x)}
= (-8/3) (5x^2 - 2x)^(-3/2) (5x - 1) as before.

2007-08-15 22:33:44 · answer #1 · answered by Scarlet Manuka 7 · 0 0

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2007-08-16 04:46:05 · answer #2 · answered by Anonymous · 0 0

8/3. (-(10x-2)/2sqrt(5x^2-2x)) (5x^2-2x))

2007-08-16 04:57:44 · answer #3 · answered by iyiogrenci 6 · 0 0

can you give the answer with full working please

2007-08-16 05:31:29 · answer #4 · answered by Anonymous · 0 0

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