Math Problem Statement

Find the derivative of f(x)=9x^2 _x^3

Solution

It seems like there is a typo in the function you've provided. I assume you meant to write f(x)=9x2x3f(x) = 9x^2 - x^3. I'll proceed with finding the derivative of this function.

The function is: f(x)=9x2x3f(x) = 9x^2 - x^3

To find the derivative f(x)f'(x), we differentiate each term of the function with respect to xx:

  1. The derivative of 9x29x^2 is 18x18x.
  2. The derivative of x3-x^3 is 3x2-3x^2.

So, the derivative of the function is: f(x)=18x3x2f'(x) = 18x - 3x^2

Would you like any details or have any questions?

Here are 5 related questions for further practice:

  1. What is the derivative of f(x)=5x3+2x2xf(x) = 5x^3 + 2x^2 - x?
  2. Find the second derivative of f(x)=9x2x3f(x) = 9x^2 - x^3.
  3. Calculate the derivative of g(x)=x44x2+7g(x) = x^4 - 4x^2 + 7.
  4. What is the slope of the tangent line to the curve f(x)=9x2x3f(x) = 9x^2 - x^3 at x=2x = 2?
  5. Find the critical points of f(x)=9x2x3f(x) = 9x^2 - x^3.

Tip: Always check your function for typos or errors before differentiating, as a small mistake can change the entire solution!

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Polynomials

Formulas

Power rule: d/dx [x^n] = n * x^(n-1)

Theorems

Basic Differentiation Rules

Suitable Grade Level

Grades 10-12