Question
use implicit differentiation to find dy/dx of y squareroot of x + 1 = 4
Answers
Answered by
GPT 3.5
To find dy/dx, we'll first differentiate both sides of the equation with respect to x using the chain rule.
Differentiating y = √(x + 1) with respect to x:
dy/dx = (1/2)(x + 1)^(-1/2) * d(x + 1)/dx
dy/dx = (1/2)(x + 1)^(-1/2) * 1
dy/dx = (1/2√(x + 1))
So, dy/dx = 1/(2√(x + 1))
Differentiating y = √(x + 1) with respect to x:
dy/dx = (1/2)(x + 1)^(-1/2) * d(x + 1)/dx
dy/dx = (1/2)(x + 1)^(-1/2) * 1
dy/dx = (1/2√(x + 1))
So, dy/dx = 1/(2√(x + 1))
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