Calculus
posted by Becky .
Find the derivative of m(x)=1/(x+1) by using the definition of the derivative.

we want the limit as h>0 of
[m(x+h)m(x)]/h
= [1/(x+1+h)  1/(x+1)]/h
= [(x+1)  (x+1+h)] / h(x+1)(x+1+h)
= h/h * 1/(x+1)(x+1+h)
> 1/(x+1)^2
Respond to this Question
Similar Questions

Math
How would I find the derivative of x^2 + 3x using the definition of the derivative? 
Calculus derivatives
f(a) = a + √a (a) Find the derivative of the function using the definition of derivative. 
Calculus  derivatives
Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the derivative … 
calculus
You are given the following function. f(x)= (8+x)/(18x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function? 
calculus
Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation) 
Calculus
Find the derivative of the function using the definition of a derivative. F(x)=squareroot(13x) Please show work for understanding, thank you! :) 
Calculus
1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^1 x is 1/(x*sqrt(x^2 1)). … 
Math (Derivative)
Computer the derivative of f(x)=x(1/x) for x>0 using the definition of the derivative. 
Math (Derivative)
Compute derivative using the definition of the derivative. f(x)=1+1/x^2 1+ 1/(x+h)^2  (1+ 1/(x^2))  divide by h and multiply by reciprocal 1/h(x+h)^2  1/hx^2 Next I expanded it and got this messy huge number and multiply the … 
Calculus
Please help me. 1. Use the definition of the derivative to find f'(x), if f(x)=x^2 2.Find the derivative of y=3t^5  5√t + 7/t