Math
posted by Jessica .
How would I find the derivative of x^2 + 3x using the definition of the derivative?

d/dx x^2+3x = 2x+3

the derivative of a function f(x) is
Limit [f(x+h)  f(x)]/h
h> 0
so derivative of x^2 + 3x =
Lim[(x+h)^2 + 3(x+h)  x^2  3x]/h =
h> 0
Lim [2hx + h^2 + 3h]/h =
h> 0
Lim [2x + h + 3\]
h> 0
= 2x + 3
Respond to this Question
Similar Questions

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 … 
math
find derivative using limit definition: f(x) = x  sqrt(x) so f'(x) = lim h>0 [f(x+h)  f(x)]/h but I keep trying to solve by multiplying by the conjugate but I can't figure it out..there's nothing that can be cancelled or anything … 
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 m(x)=1/(x+1) by using the definition of the derivative. 
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 … 
Math Derivative
Find derivative of f(x)=g(h(x)) Would the derivative be something like: g'(h(x))*h'(x) ?