metadata
source: knowledge_base
topic: calculus
class_level: class_12
difficulty: advanced
Calculus Fundamentals: Power Rule: d/dx[x^n]=nx^(n-1). Product Rule: d/dx[fg]=f'g+fg'. Chain Rule: d/dx[f(g(x))]=f'(g(x))*g'(x). Quotient Rule: d/dx[f/g]=(f'g-fg')/g^2. d/dx[sin(x)]=cos(x), d/dx[cos(x)]=-sin(x), d/dx[e^x]=e^x, d/dx[ln(x)]=1/x. integral(x^n dx)=x^(n+1)/(n+1)+C, integral(e^x dx)=e^x+C. Fundamental Theorem: integral[a to b]f(x)dx=F(b)-F(a) where F'(x)=f(x).