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Question
Differentiate the following w.r.t. x: `sqrt(x^2 + 4x - 7)`.
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Solution
y = `sqrt(x^2 + 4x - 7) [sqrt(x) = 1/(2sqrtx)]`
Differentiating w.r.t. x, we get
`"dy"/"dx" = (1)/(2sqrt(x^2 + 4x - 7)). "d"/"dx"(x^2 + 4x - 7)`
`= (1)/(2sqrt(x^2 + 4x - 7)).("d"/"dx"x^2 + "d"/"dx"4x - "d"/"dx"7)`
= `(1)/(2sqrt(x^2 + 4x - 7)).(2x + 4 - 0)`
= `(2(x + 2))/(2sqrt(x^2 + 4x - 7)`
= `((x + 2))/(sqrt(x^2 + 4x - 7)`
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