Best answer:
f(x) = √(x) + 2
You can think of square root as being the 1/2 power:
f(x) = x^(1/2) + 2
When getting the first derivative from polynomials (and the same rule applies here), your new coefficient for each term is the old coefficient times the exponent. Then you subtract the exponent by 1.
Any constant terms gets...
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Best answer: f(x) = √(x) + 2
You can think of square root as being the 1/2 power:
f(x) = x^(1/2) + 2
When getting the first derivative from polynomials (and the same rule applies here), your new coefficient for each term is the old coefficient times the exponent. Then you subtract the exponent by 1.
Any constant terms gets dropped out. So that 2 goes away, leaving the x to the 1/2 power. coefficient of x is 1, times 1/2 is 1/2, so that's your new coefficient. Then subtract the exponent by 1 to get:
f'(x) = (1/2)x^(-1/2)
Putting that back into radical form, the square root is now in the denominator due to the negative coefficient:
f'(x) = 1 / (2√x)
Substitute 7 for x:
f'(7) = 1 / (2√7)
And rationalize the denominator:
f'(7) = √(7) / 14
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2 days ago