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misconception when differentiating rational functions that the derivatives of the numerator and theIt is a common()does not equaldenominator can be calculated separately. The derivative ofAlthough the derivative is an operator, it does not follow the same rules as some other mathematical operators such asnexponents, in whichyхх?Let h(x)h'The derivatives of the numerator and the denominator are both equal to 2x. It is incorrect to say2xequals- 12хx2Use the quotient rule to find the correct derivative of h(x)х2—2h(x)=

Question
misconception when differentiating rational functions that the derivatives of the numerator and the
It is a common
()
does not equal
denominator can be calculated separately. The derivative of
Although the derivative is an operator, it does not follow the same rules as some other mathematical operators such as
n
exponents, in which
y
х
х?
Let h(x)
h'
The derivatives of the numerator and the denominator are both equal to 2x. It is incorrect to say
2x
equals
- 1
2х
x2
Use the quotient rule to find the correct derivative of h(x)
х2—2
h(x)=
help_outline

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misconception when differentiating rational functions that the derivatives of the numerator and the It is a common () does not equal denominator can be calculated separately. The derivative of Although the derivative is an operator, it does not follow the same rules as some other mathematical operators such as n exponents, in which y х х? Let h(x) h' The derivatives of the numerator and the denominator are both equal to 2x. It is incorrect to say 2x equals - 1 2х x2 Use the quotient rule to find the correct derivative of h(x) х2—2 h(x)=

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Step 1

We apply quotient rule on h(x)

(u/v)'= (u'v-uv')...

x2
h(x)=
x2-2
h'(x)= _(X*Y(x°-2)-x'(x2-2)"
(x2-2)2
help_outline

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x2 h(x)= x2-2 h'(x)= _(X*Y(x°-2)-x'(x2-2)" (x2-2)2

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