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Question
If `y = sin^-1(1/x^3)`, then `dy/dx` = ______
Options
`-3/(x^4 sin[cos^-1(1/x^3)])`
`3/(xsqrt(x^6 - 1))`
`3/(x^4 sin[cos^-1(1/x^3)])`
`(-3)/(xsqrt(x^6 - 1))`
MCQ
Fill in the Blanks
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Solution
If `y = sin^-1(1/x^3)`, then `dy/dx` = `underline((-3)/(xsqrt(x^6 - 1)))`
Explanation:
`y = sin^-1(1/x^3)`
∴ `y = cosec^-1(x^3)`
∴ `dy/dx = (-1)/(x^3sqrt((x^3)^2 - 1)) . 3x^2 = (-3)/(xsqrt(x^6 - 1))`
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Derivative of Inverse Functions
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