| source: knowledge_base | |
| topic: calculus | |
| class_level: class_12 | |
| difficulty: advanced | |
| Calculus Fundamentals: | |
| Power Rule: d/dx[x^n]=n*x^(n-1). Product Rule: d/dx[f*g]=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). |