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Question
Differentiate the following w.r.t.x:
`sqrt(e^((3x + 2) + 5)`
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Solution
Let y = `sqrt(e^((3x + 2) + 5)`
Differentiating w.r.t. x,we get,
`"dy"/"dx" = "d"/"dx"[e^((3x + 2)) + 5]^(1/2)`
= `1/2[e^((3x + 2)) + 5]^(-1/2)."d"/"dx"[e^((3x + 2)) + 5]`
= `1/(2sqrt(e^((3x + 2)) + 5)).[e^((3x + 2)). "d"/"dx"(3x + 2) + 0]`
= `1/(2sqrt(e^((3x + 2)) + 5)).[e^((3x + 2)). (3 xx 1 + 0)]`
= `(3e^((3x + 2)))/(2sqrt(e^((3x + 2))+ 5)`.
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