Find a formula for the derivatives of the function m(x)=1/(x+1)
Please help.....Any assistance would be greatly appreciated.
Why plural? There is only one derivative of that function.
Let x+1 = u, so that
m(x) = m{u(x)}, m(u) = 1/u, and
du/dx = 1
Then use the chain rule
dm/dx = dm/du*du/dx
= -1/u^2 = -1/(x+1)^2
To find the derivative of the function m(x) = 1/(x+1), you can use the quotient rule.
The quotient rule states that if you have a function h(x) = f(x)/g(x), then its derivative is given by:
h'(x) = (f'(x) * g(x) - f(x) * g'(x)) / [g(x)]^2
In the case of m(x) = 1/(x+1), let's assign f(x) = 1 and g(x) = (x+1). Now we can find the derivatives of f(x) and g(x) and substitute them into the quotient rule formula.
First, let's find the derivative of f(x):
f'(x) = 0 (since the derivative of a constant is always 0)
Now, let's find the derivative of g(x):
g'(x) = 1 (since the derivative of x is 1)
Substituting these derivatives into the quotient rule formula, we get:
m'(x) = (0 * (x+1) - 1 * 1) / [(x+1)]^2
Simplifying this expression:
m'(x) = (-1) / [(x+1)]^2
Therefore, the derivative of the function m(x) = 1/(x+1) is m'(x) = -1/[(x+1)]^2.