How can derive this function?f(x) = 2/(9x^5+1)^5
The answer is The answer is -450x^4/(9x^5+1)^6 Can you please show why? Thank you
first write it as
f(x) = 2(9x^5 + 1)^-5
now by the chain rule ...
f ' (x) = -10(9x^5 + 1)^-6 (45x^4)
= -450x^4/(9x^5 + 1)^6
How did you get an exponent of 6??
not 6. It's -5 - 1 = -6
To derive the function f(x) = 2/(9x^5+1)^5, we can use the chain rule. The chain rule is used when we have a composition of functions.
Let's break down the function into simpler functions:
Let u = 9x^5 + 1
Rewriting f(x) using u:
f(x) = 2/u^5
Let's derive the function with respect to x using the chain rule:
Step 1: Find the derivative of u with respect to x.
du/dx = 45x^4
Step 2: Differentiate f(u) = 2/u^5 with respect to u.
df/du = d(2/u^5)/du = -10/u^6
Step 3: Multiply the derivatives found in steps 1 and 2 to get the derivative of f(x):
df/dx = df/du * du/dx = -10/u^6 * 45x^4
Substituting back u = 9x^5 + 1:
df/dx = -450x^4/(9x^5 + 1)^6
Therefore, the derivative of f(x) = 2/(9x^5+1)^5 is -450x^4/(9x^5+1)^6.