# Calculus

posted by .

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

• Calculus -

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

## Similar Questions

1. ### Math

How would I find the derivative of x^2 + 3x using the definition of the derivative?
2. ### Calculus derivatives

f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.
3. ### 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 …
4. ### calculus

You are given the following function. f(x)= (8+x)/(1-8x) (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?
5. ### 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)
6. ### Calculus

Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)
7. ### 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)). …
8. ### Math (Derivative)

Computer the derivative of f(x)=x-(1/x) for x>0 using the definition of the derivative.
9. ### 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 …
10. ### 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

More Similar Questions