Question 1

What is the difference between differentiation and integration?

Accepted Answer

Differentiation finds the rate of change (slope). Integration is the reverse, finding the area under a curve or recovering the original function.

Question 2

What is the power rule for derivatives?

Accepted Answer

d/dx(x^n) = n x^(n-1). Example: d/dx(x^3) = 3x^2. Works for any real exponent.

Question 3

Why do we add + C in integration?

Accepted Answer

Because the derivative of any constant is zero, infinitely many functions have the same derivative. C represents this arbitrary constant.

Question 4

What is definite vs indefinite integration?

Accepted Answer

Indefinite integral gives a function F(x) + C. Definite integral from a to b gives a number: F(b) - F(a), representing the area.

Question 5

What is the chain rule?

Accepted Answer

d/dx[f(g(x))] = f'(g(x)) x g'(x). Used for composite functions. Example: d/dx[sin(x^2)] = cos(x^2) x 2x.

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