Mathematics
Calculus: Derivatives & Integrals
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This set covers the most common derivative and integral rules in calculus, including power, product, quotient, and chain rules, as well as standard integrals and basic functions. Ideal for students preparing for exams or refreshing foundational concepts.
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Derivative of xⁿ
n·xⁿ⁻¹
Derivative of sin(x)
cos(x)
Derivative of cos(x)
-sin(x)
Derivative of tan(x)
sec²(x)
Derivative of e^x
e^x
Derivative of ln(x)
1/x
Derivative of a constant
0
Product Rule
d(uv)/dx = u'v + uv'
Quotient Rule
d(u/v)/dx = (u'v - uv') / v²
Chain Rule
d(f(g(x)))/dx = f'(g(x))·g'(x)
Derivative of sec(x)
sec(x)·tan(x)
Derivative of csc(x)
-csc(x)·cot(x)
Derivative of cot(x)
-csc²(x)
∫xⁿ dx (n ≠ -1)
(xⁿ⁺¹)/(n+1) + C
∫1/x dx
ln
∫e^x dx
e^x + C
∫a^x dx
(a^x) / ln(a) + C
∫sin(x) dx
-cos(x) + C
∫cos(x) dx
sin(x) + C
∫sec²(x) dx
tan(x) + C
∫csc²(x) dx
-cot(x) + C
∫sec(x)tan(x) dx
sec(x) + C
∫csc(x)cot(x) dx
-csc(x) + C
∫1/(1 + x²) dx
arctan(x) + C
∫1/√(1 - x²) dx
arcsin(x) + C
Fundamental Theorem of Calculus
∫ₐᵇ f(x) dx = F(b) - F(a), where F'(x) = f(x)