Math Problem Statement

Basic Differentiation: o Differentiate the following functions with respect to x: ▪ f(x) = 3x2+2x+1

Solution

To differentiate the function f(x)=3x2+2x+1f(x) = 3x^2 + 2x + 1 with respect to xx, we apply the basic rules of differentiation.

Function:

f(x)=3x2+2x+1f(x) = 3x^2 + 2x + 1

Step-by-step differentiation:

  1. Differentiate 3x23x^2: ddx(3x2)=32x21=6x\frac{d}{dx}(3x^2) = 3 \cdot 2x^{2-1} = 6x

  2. Differentiate 2x2x: ddx(2x)=21x11=2\frac{d}{dx}(2x) = 2 \cdot 1x^{1-1} = 2

  3. Differentiate the constant 11: ddx(1)=0\frac{d}{dx}(1) = 0

Final result:

f(x)=6x+2f'(x) = 6x + 2

The derivative of the function f(x)=3x2+2x+1f(x) = 3x^2 + 2x + 1 is f(x)=6x+2f'(x) = 6x + 2.

Would you like more details on how these rules work or have any other questions?

Here are 5 related questions for further exploration:

  1. What is the derivative of g(x)=5x3+4x2+3x+2g(x) = 5x^3 + 4x^2 + 3x + 2?
  2. How do we differentiate trigonometric functions like sin(x)\sin(x)?
  3. What is the second derivative of f(x)=3x2+2x+1f(x) = 3x^2 + 2x + 1?
  4. How does the chain rule apply in differentiation?
  5. What is the derivative of f(x)=exf(x) = e^x?

Tip: When differentiating powers of xx, apply the power rule: ddx(xn)=nxn1\frac{d}{dx}(x^n) = nx^{n-1}.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Differentiation
Calculus

Formulas

Power Rule: d/dx(x^n) = nx^{n-1}
Sum Rule: d/dx(f(x) + g(x)) = f'(x) + g'(x)

Theorems

Basic Differentiation Theorem

Suitable Grade Level

Grades 10-12