Calculus
Quick Reference

Derivatives, integrals, and common rules. From basics to advanced techniques.

Derivatives

Basic Rules

d/dx [c] = 0
d/dx [x^n] = nx^(n-1)
d/dx [e^x] = e^x
d/dx [ln(x)] = 1/x

Trigonometric

d/dx [sin(x)] = cos(x)
d/dx [cos(x)] = -sin(x)
d/dx [tan(x)] = sec²(x)

Chain Rule

d/dx [f(g(x))] = f'(g(x)) · g'(x)

Integrals

Basic Integrals

∫ x^n dx = x^(n+1)/(n+1) + C
∫ e^x dx = e^x + C
∫ 1/x dx = ln|x| + C

Trigonometric

∫ sin(x) dx = -cos(x) + C
∫ cos(x) dx = sin(x) + C
∫ sec²(x) dx = tan(x) + C

Integration by Parts

∫ u dv = uv - ∫ v du

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