Math Problem Statement

create me a random equation in latex about derivative and explain how u got the answer

Solution

Here's a random equation involving derivatives, written in LaTeX:

f(x)=ddx(x3+2x25x+7)=3x2+4x5f'(x) = \frac{d}{dx} \left( x^3 + 2x^2 - 5x + 7 \right) = 3x^2 + 4x - 5

Explanation

  1. Original Function: f(x)=x3+2x25x+7f(x) = x^3 + 2x^2 - 5x + 7

    This is a polynomial function where the highest degree is 3 (cubic polynomial).

  2. Taking the Derivative:

    • The derivative of xnx^n with respect to xx is nxn1n \cdot x^{n-1}.
    • Applying this rule:
      • ddx(x3)=3x2\frac{d}{dx} \left( x^3 \right) = 3x^2
      • ddx(2x2)=4x\frac{d}{dx} \left( 2x^2 \right) = 4x
      • ddx(5x)=5\frac{d}{dx} \left( -5x \right) = -5
      • The derivative of the constant 77 is 00.
  3. Final Answer:

    • Combine these results to get the derivative: f(x)=3x2+4x5f'(x) = 3x^2 + 4x - 5

Would you like more details or have any questions?

Related Questions:

  1. How do you find the derivative of trigonometric functions?
  2. What is the geometric interpretation of a derivative?
  3. How do you calculate higher-order derivatives?
  4. What is the chain rule in differentiation?
  5. How does the derivative apply to real-world problems?

Tip: When differentiating, always simplify the function first if possible; this can make the differentiation process easier.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Derivatives
Polynomial functions

Formulas

Power rule of differentiation

Theorems

-

Suitable Grade Level

Grades 10-12