Core derivative and integration rules used across intro calculus courses.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- Power rule for derivatives: d/dx[x^n] = ?
- n*x^(n-1)
- Product rule: d/dx[f(x)*g(x)] = ?
- f'(x)*g(x) + f(x)*g'(x)
- Quotient rule: d/dx[f(x)/g(x)] = ?
- [f'(x)*g(x) - f(x)*g'(x)] / [g(x)]^2
- Chain rule: d/dx[f(g(x))] = ?
- f'(g(x)) * g'(x)
- d/dx[sin(x)] = ?
- cos(x)
- d/dx[cos(x)] = ?
- -sin(x)
- d/dx[tan(x)] = ?
- sec^2(x)
- d/dx[cot(x)] = ?
- -csc^2(x)
- d/dx[sec(x)] = ?
- sec(x)*tan(x)
- d/dx[csc(x)] = ?
- -csc(x)*cot(x)
- d/dx[e^x] = ?
- e^x
- d/dx[a^x] = ?
- a^x * ln(a)
- d/dx[ln(x)] = ?
- 1/x
- d/dx[log_a(x)] = ?
- 1/(x*ln(a))
- d/dx[sin^(-1)(x)] = ?
- 1/sqrt(1-x^2)