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The derivative of (x2–1)/x is
- a)1 + 1/x2
- b)1 – 1/x2
- c)1/x2
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The derivative of (x21)/x isa)1 + 1/x2b)1 1/x2c)1/x2d)none of theseCo...
Denominator wale x ko distribute kro fir 1st term wala ek x cancel hojayega fir derivative lelo
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The derivative of (x21)/x isa)1 + 1/x2b)1 1/x2c)1/x2d)none of theseCo...
Derivative of (x^2+1)/x:
To find the derivative of the given expression, we can use the quotient rule.
The quotient rule states that if we have a function f(x) = g(x)/h(x), then the derivative of f(x) is given by:
f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2
In this case, g(x) = x^2 + 1 and h(x) = x.
Applying the quotient rule:
Let's find the derivative of (x^2 + 1)/x using the quotient rule.
Step 1: Find g'(x) and h'(x).
g'(x) = d/dx (x^2 + 1) = 2x
h'(x) = d/dx (x) = 1
Step 2: Apply the quotient rule.
f'(x) = (2x * x - (x^2 + 1) * 1) / (x^2)^2 = (2x^2 - (x^2 + 1)) / x^2 = (x^2 - 1) / x^2
Therefore, the derivative of (x^2 + 1)/x is (x^2 - 1)/x^2.
Comparing with the options:
Now let's compare the derived expression with the given options to find the correct answer.
Option A: 1
Option B: 1/x^2
Option C: 1/x^2
Option D: none of these
Comparing the derived expression (x^2 - 1)/x^2 with the options, we can see that none of the options match the derived expression. Therefore, the correct answer is none of these (Option D).
Hence, the given answer is incorrect.
To find the derivative of the given expression, we can use the quotient rule.
The quotient rule states that if we have a function f(x) = g(x)/h(x), then the derivative of f(x) is given by:
f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))^2
In this case, g(x) = x^2 + 1 and h(x) = x.
Applying the quotient rule:
Let's find the derivative of (x^2 + 1)/x using the quotient rule.
Step 1: Find g'(x) and h'(x).
g'(x) = d/dx (x^2 + 1) = 2x
h'(x) = d/dx (x) = 1
Step 2: Apply the quotient rule.
f'(x) = (2x * x - (x^2 + 1) * 1) / (x^2)^2 = (2x^2 - (x^2 + 1)) / x^2 = (x^2 - 1) / x^2
Therefore, the derivative of (x^2 + 1)/x is (x^2 - 1)/x^2.
Comparing with the options:
Now let's compare the derived expression with the given options to find the correct answer.
Option A: 1
Option B: 1/x^2
Option C: 1/x^2
Option D: none of these
Comparing the derived expression (x^2 - 1)/x^2 with the options, we can see that none of the options match the derived expression. Therefore, the correct answer is none of these (Option D).
Hence, the given answer is incorrect.
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The derivative of (x21)/x isa)1 + 1/x2b)1 1/x2c)1/x2d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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