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Question
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Solution
Let u = sin x2
`("d"u)/("d"x)` = cos(x2) × 2x
`("d"u)/("d"x)` = 2x cos(x2)
Let v = x2
`("dv")/("d"x)` = 2x
`(("d"u)/("d"x))/(("dv")/("d"x)) = (2x cos(x^2))/(2x)`
`("d"u)/("dv") = cos (x^2)`
`("d"(sin x^2))/("d"(x^2)) = cos (x^2)`
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