# The derivative of [g(x)]^2 is equal to [g'(x)']^2. true or false?

hala718 | Certified Educator

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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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neela | Student

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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