If \(y = (1 + x)^2\), find \(\frac{dy}{dx}\)
Question 1 Report
If \(y = (1 + x)^2\), find \(\frac{dy}{dx}\)
Answer Details
To find dy/dx for y = (1 + x)^2, we can use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x), where f'(g(x)) is the derivative of the outer function evaluated at g(x), and g'(x) is the derivative of the inner function evaluated at x.
In this case, we can let f(x) = x^2 and g(x) = 1 + x, so that y = f(g(x)) = (1 + x)^2. Then, we can find the derivatives of f(x) and g(x) as follows:
f'(x) = 2x
g'(x) = 1
Using the chain rule, we can now find dy/dx:
dy/dx = f'(g(x)) * g'(x) = 2(1 + x) * 1 = 2 + 2x
Therefore, dy/dx = 2 + 2x.
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