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Find The First Derivatives of The Following Function Calculator

Reviewed by Calculator Editorial Team

This calculator helps you find the first derivative of any function using calculus rules. Whether you're studying calculus or need to solve real-world problems, this tool provides step-by-step results and explanations.

How to Use This Calculator

To find the first derivative of a function:

  1. Enter your function in the input field (e.g., "x^2 + 3x - 5")
  2. Click "Calculate" to see the derivative
  3. Review the step-by-step solution and graph

Note: This calculator supports basic algebraic functions. For more complex functions, you may need to use advanced calculus techniques.

Basic Calculus Rules

Power Rule

If f(x) = x^n, then f'(x) = n*x^(n-1)

f(x) = x^n
f'(x) = n*x^(n-1)

Sum/Difference Rule

The derivative of a sum (or difference) is the sum (or difference) of the derivatives.

f(x) = g(x) ± h(x)
f'(x) = g'(x) ± h'(x)

Product Rule

If f(x) = g(x)*h(x), then f'(x) = g'(x)*h(x) + g(x)*h'(x)

f(x) = g(x)*h(x)
f'(x) = g'(x)*h(x) + g(x)*h'(x)

Quotient Rule

If f(x) = g(x)/h(x), then f'(x) = [g'(x)*h(x) - g(x)*h'(x)] / [h(x)]^2

f(x) = g(x)/h(x)
f'(x) = [g'(x)*h(x) - g(x)*h'(x)] / [h(x)]^2

Chain Rule

If f(x) = g(h(x)), then f'(x) = g'(h(x))*h'(x)

f(x) = g(h(x))
f'(x) = g'(h(x))*h'(x)

Worked Examples

Example 1: Simple Polynomial

Find the derivative of f(x) = 3x^4 - 2x^2 + 5x - 7

Solution:

  1. Apply the power rule to each term:
    • 3x^4 → 12x^3
    • -2x^2 → -4x
    • 5x → 5
    • -7 → 0
  2. Combine the results: f'(x) = 12x^3 - 4x + 5

Example 2: Product of Functions

Find the derivative of f(x) = x*sin(x)

Solution:

  1. Identify g(x) = x and h(x) = sin(x)
  2. Find derivatives: g'(x) = 1 and h'(x) = cos(x)
  3. Apply product rule: f'(x) = 1*sin(x) + x*cos(x) = sin(x) + x*cos(x)

FAQ

What types of functions can this calculator handle?
This calculator handles basic algebraic functions including polynomials, trigonometric functions, exponential functions, and logarithmic functions. For more complex functions, you may need to use advanced calculus techniques.
How accurate are the results?
The calculator uses standard calculus rules to compute derivatives. The results are mathematically accurate based on the input function and the rules applied.
Can I use this calculator for homework or exams?
Yes, you can use this calculator to check your work or understand how to solve derivative problems. However, always verify your understanding of the calculus rules being applied.