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Calculus
University
Calculus (University Level)
Power Rule for Derivatives
Find the derivative of x raised to the power n
Standard Formula
d/dx(xⁿ) = n × x^(n-1)
Interactive Sandbox
Live Reactive
Adjust values in real-time and observe mathematical cause-and-effect
n
120
x
120
Live EquationFormula Proof
d/dx(2ⁿ) = 3 × 2^(3-1) = 12
Tangent Line dy/dx
Calculated Solution
12
Direct computational model evaluating Power Rule for Derivatives.
Variable Mechanics
Roles, constraints & impacts
2 Params
n
Exponent
Exponent
ImpactPrimary formula parameter
ConstraintReal number
x
Variable value
Variable value
ImpactPrimary formula parameter
ConstraintReal number
At a Glance
Gotchas, units & real-world use
Essential
Formula Nature & Mechanics
Direct computational model evaluating Power Rule for Derivatives.
Common Mistakes & Traps
- Ensure all input measurements share consistent units before calculating.
- Check for denominator values approaching zero to prevent undefined division.
- Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).
Dimensional Analysis & Units
Direct evaluation matching formula variable dimensions.
Real-World & Industry Application
Widely utilized across modern calculus applications, academic analysis, and engineering estimations.
Worked Example: Power Rule for Derivatives
Given:
- n = 3
- x = 2
- d/dx(x³) = 3x²
- At x = 2: 3(2)² = 3(4) = 12
Answer: 12
Frequently Asked Questions
What is the Power Rule for Derivatives formula?
d/dx(xⁿ) = n × x^(n-1). Find the derivative of x raised to the power n.
How do I calculate Power Rule for Derivatives?
Enter Exponent (n), Variable value (x) into the calculator. It applies d/dx(xⁿ) = n × x^(n-1) and shows every step of the working.
Related Calculus Calculators
Definite Integral (Power Rule)∫[a to b] x^n dx = [x^(n+1)/(n+1)]|[a to b]Partial Derivative∂f/∂x = lim[h→0] (f(x+h,y) - f(x,y))/hChain Rule (Derivative)d/dx[f(g(x))] = f'(g(x)) · g'(x)Product Rule (Derivative)d/dx[f·g] = f'·g + f·g'Quotient Rule (Derivative)d/dx[f/g] = (f'·g − f·g') / g²Derivative of sin(ax)d/dx[sin(ax)] = a·cos(ax)
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