Derivative Engine
Symbolic differentiation of any expression in x — with higher-order derivatives, point evaluation, and the tangent line drawn on the graph. Covers §5.7–5.14 of the calculus material.
Supported syntax
x^2, 3x+1, sin(x), cos(x), tan(x), sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, ln(x), log(x), exp(x), sqrt(x), |x|, pi, e — implicit multiplication works: 2x, 3sin(x), (x+1)(x-2)
Differentiate
The applied rules (product, quotient, chain, power) are reported in the steps.
f(x) in steel; the tangent line at the chosen point in red (dashed). FIG. T25-1
The derivative at a point is the slope of the tangent line there: f′(a) = limh→0 [f(a+h) − f(a)]/h. The tangent line is y = f(a) + f′(a)(x − a).