To find the derivative of the function \(\frac{x^4}{{(3x-8)}^2}\), we can use the quotient rule.
The quotient rule states that if we have a function \(f(x) = \frac{g(x)}{h(x)}\), then the derivative of \(f(x)\) is given by:
\[
f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{{(h(x))}^2}
\]
In this case, \(g(x) = x^4\) and \(h(x) = (3x-8)^2\).
Using the power rule, we can find \(g'(x)\):
\[
g'(x) = 4x^{4-1} = 4x^3
\]
Using the chain rule, we can find \(h'(x)\):
\[
h'(x) = 2(3x-8)(3) = 6(3x-8)
\]
Now we can substitute these values into the quotient rule formula:
\[
f'(x) = \frac{(4x^3)(3x-8) - (x^4)(6(3x-8))}{{(3x-8)}^2}
\]
Simplifying this equation will give you the derivative of the function.
What is the derivative of (x^4)/(3x-8)^2
1 answer