CaLaun
Calculus, one step at a time
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Derivatives
Integrals
Limits
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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