# Calculus

posted by .

Find the derivative of the following function f(x)=(x-3/2x+3)^2

• Calculus -

Assuming the usual carelessness with parentheses, I gather you mean

f(x) = ((x-3)/(2x+3))^2

If f = u^2, f' = 2u u'

So, f' = 2(x-3)/(2x+3) * ((x-3)/(2x+3))'
= 2(x-3)/(2x+3) * [(2x+3)-2(x-3)/(2x+3)^2]
= 2(x-3)/(2x+3)*(9/(2x+3)^2)
= 18(x-3)/(2x+3)^3

## Similar Questions

1. ### Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that …
2. ### 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?
3. ### calculus

At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous …
4. ### Calculus (Urgent!!)

Hello everyone, I need help with the following problems. Find the partial derivative of the following: 1) f(X1, X2) = X1^1/2*X2^3/4 2) f(x1,x2,x3) = ln(x1)x2 + 3x3 3) f(x,y) = 3x + 4y 4) f(x,y) = x^1/2 +x/y + y/x Find the maximum of …
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

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative Please show me how u got this!!
7. ### Calculus

Find the derivative of the following function: f(x)= 10x-3/5x +6x
8. ### Calculus

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. intergral s^2/(1+3s^4) ds from sqrtx to 1 F'(x)=?
9. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
10. ### Calculus

Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of …

More Similar Questions