The derivative of [g(x)]^2 is equal to [g'(x)']^2. true or false?
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Given that the derivative of the function g(x)^2 is g'(x)'^2
We need to determine if the statemtn if true or false.
Let us determine the derivative of [g(x)]^2
We know that:
[g(x)]^2 = g(x) * g(x)
Then we will use the product rule to find the derivative.
Then, we know that:
==>{ [g(x)]2}' = g'(x) * g(x) + g(x) * g'(x)
= 2g(x)*g'(x)
==> The derivative of g(x)]^2 = 2g(x)*g'(x)
Then the statement is false.
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Q: The derivative of [g(x)]^2 is equal to [g'(x)']^2. true or false.
Solution:
False.
Let y = [g(x)]^2.
We differentiate with respect to x.
dy/dx = d/dx { [g(x)]^2}.
dy/dx = 2*g(x)* d/dx{g(x)}.
dy/dx = 2g(x)* g'x), as d/dx {g(x) } = g'(x).
Therefore derivative of [g(x)]^2 = 2*g(x)*g'(x).
It is not [g'(x)']^2.
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