find f'(a) for f(x)=1/sqrt(13-7x)
i got my answer to be 7 / (7(13-7x)sqrt(13-7x))
but it says i am wrong
please help
To find the derivative of the function f(x) = 1/√(13-7x), we can use the chain rule.
Let's start by applying the power rule.
f(x) = (13-7x)^(-1/2)
Now, we can find the derivative using the chain rule. The chain rule states that if we have a composition of functions f(g(x)), then the derivative is given by f'(g(x)) * g'(x).
In our case, g(x) = 13-7x, and f(g) = g^(-1/2).
First, let's find the derivative of g(x):
g'(x) = -7
Now, let's find the derivative of f(g):
f'(g) = (-1/2) * g^(-3/2)
Now, we can combine the results to find the derivative of the original function f(x):
f'(x) = f'(g) * g'(x) = (-1/2) * (13-7x)^(-3/2) * (-7)
f'(x) = 7 / [2(13-7x)^(3/2)]
To find f'(a), we substitute a into the derivative function:
f'(a) = 7 / [2(13-7a)^(3/2)]
Therefore, the correct answer is 7 / [2(13-7a)^(3/2)].