If f(x)=(4x+8)^-2, Find f'(x)
-2(4x+8)^-3 * 4 = -8(4x+8)^3
Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx.
y=√sinx
√ is square root.
This has nothing to do with your previously posted question.
u(x) = g(x) = sin x
f(u) = sqrt u
y = sqrt(sinx) = sqrt[g(x)]
To find the derivative of the function f(x) = (4x + 8)^-2, we can use the chain rule. The chain rule states that if we have a function within a function, we need to differentiate both functions and multiply their derivatives together.
Let's break down the steps to find f'(x):
Step 1: Identify the inner function.
In this case, the inner function is (4x + 8).
Step 2: Differentiate the inner function.
To differentiate (4x + 8), we need to remember that the derivative of x is 1. Therefore, the derivative of 4x is simply 4.
Step 3: Elevate the inner function to the power of -2.
Now that we have differentiated the inner function, we need to multiply it by -2 and subtract 1 from the exponent to get the derivative of the outer function.
The derivative of (4x + 8)^-2 can be found using the following formula:
f'(x) = -2 * (4x + 8)^-3 * 4
Simplifying this expression, we get:
f'(x) = -8 / (4x + 8)^3
So, the derivative of f(x) = (4x + 8)^-2 is f'(x) = -8 / (4x + 8)^3.