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- Power rule basics diff(x^5, x)
- Chain rule with trig diff(sin(x^2), x)
- Product rule diff(x^2 * ln(x), x)
- Quotient rule diff(x/(x^2 + 1), x)
- Nested chain rule diff(cos(x)^7, x)
- Multiple rules combined diff(x*cos(x)*sin(x), x)
- Exponential functions diff(exp(x^2), x)
- Logarithmic differentiation diff(x^x, x)
- Inverse trig functions diff(arctan(x), x)
- Implicit style diff(sqrt(1 - x^2), x)
- Power rule for integrals integrate(x^3, x)
- Basic trig integral integrate(cos(x), x)
- Natural log pattern integrate(1/x, x)
- U-sub with chain rule integrate(x*exp(x^2), x)
- Trig substitution prep integrate(sin(x)*cos(x), x)
- Integration by parts integrate(x*exp(x), x)
- Partial fractions integrate(1/(x^2 - 1), x)
- Trig identities integrate(sin(x)^2, x)
- Inverse trig result integrate(1/sqrt(1 - x^2), x)
- Hyperbolic functions integrate(sinh(x), x)
- Direct substitution limit(x^2 + 2*x, x, 3)
- Continuous function limit(cos(x), x, 0)
- Classic indeterminate form limit((x^2 - 4)/(x - 2), x, 2)
- Factor and cancel limit((x^2 - 1)/(x - 1), x, 1)
- Fundamental trig limit limit(sin(x)/x, x, 0)
- Exponential limit limit((exp(x) - 1)/x, x, 0)
- Limit at infinity limit(1/x, x, oo)
- Rational function limit((2*x^2 + 3)/(x^2 - 1), x, oo)
- Exponential dominance limit(exp(x)/x^2, x, oo)
- Definition of e limit((1 + 1/x)^x, x, oo)
- One-sided approach limit(1/x, x, 0, "+")
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