Use the table below to evaluate d/dx [f[g(2x)]] at x = 1
x 1 2 3 4
f(x) 6 1 8 2
f '(x) 6 1 8 2
g(x) 1 4 4 3
g '(x) 9 5 5 -4
I don't know how to continue with this question. i know [g(2x)]=8...pretty sure
How do you get g(2x)=8 at x=1?
g(2) = 4
Anyway, take a peek here and I think it will become clear. Just be sure to include that final 2 for the g(2x) instead of g(x).
http://www.calculus-help.com/6-table-derivatives/
scroll down to the end.
To evaluate the derivative d/dx [f[g(2x)]] at x = 1, we need to follow the chain rule of differentiation. The chain rule states that if we have a composition of functions, such as f[g(2x)], the derivative can be obtained by multiplying the derivative of the outer function (f') with the derivative of the inner function (g').
Let's break down the steps to calculate the derivative at x = 1:
Step 1: Calculate g(2x)
To find [g(2x)], substitute the value of x into the g(x) function. Since x = 1, we have:
g(2x) = g(2 * 1) = g(2) = 4 (according to the given table)
Step 2: Calculate f[g(2x)]
Now that we know [g(2x)] is equal to 4, we can substitute it into the f(x) function. So, we have:
f[g(2x)] = f[4]
Step 3: Calculate the derivative of f[g(2x)]
To find the derivative of f[g(2x)], we can differentiate the f(x) function with respect to x and substitute the value of [g(2x)] into it.
Since [g(2x)] is equal to 4, we can substitute it into the f'(x) function from the given table:
f'(x) = 1 when x = 4 (according to the given table)
Therefore, d/dx [f[g(2x)]] = 1 when [g(2x)] = 4.
In this case, since [g(2x)] is equal to 4, the derivative evaluated at x = 1 is 1.