Calc 494

Differentiation finds the instantaneous rate of change (slope) of a function. Integration is the reverse operation, finding the area under a curve or the antiderivative. These fundamental concepts are essential in physics, engineering, economics, and all quantitative sciences.

1. 1

   Select Operation

   Choose derivative or integral

2. 2

   Enter Function

   Input the mathematical function (e.g., x^2, sin(x), e^x)

3. 3

   Apply Rules

   The calculator applies appropriate differentiation or integration rules

4. 4

   View Solution

   The result displays with detailed solution steps

• 1

  Power rule for derivatives: d/dx(x^n) = n x^(n-1)

• 2

  Chain rule: d/dx[f(g(x))] = f'(g(x)) x g'(x)

• 3

  Always add constant of integration C for indefinite integrals

• 4

  Integral of 1/x is ln|x| + C (absolute value is important)

• Forgetting the constant of integration C - indefinite integrals have infinitely many solutions

• Applying power rule when n = -1 - integral of x^(-1) is ln|x| + C, not x^0/0

• Forgetting the chain rule - d/dx[sin(2x)] = 2cos(2x), not just cos(2x)

• Confusing d/dx with partial derivatives - d/dx is for single variable functions