Results
Symbolic:
Numeric (evaluated):
Tangent:
This tool is provided for learning. Double-check expressions before citing them in coursework.
How it's calculated
Graph & tangent
Teacher notes
Static example before you calculate
This example is shown as readable page content. It does not run the calculator or change the inputs until you press Compute.
- Input example:
f(x)=sin(x)*exp(x), first derivative, evaluated atx₀=0. - Derivative reading: apply the product rule to get
f′(x)=exp(x)*(sin(x)+cos(x)). - Point reading: at
x=0, the slope is1, so the tangent line isy=x. - Graph reading: the tangent should touch the curve near the origin; use the canvas after calculation to check the local slope visually.
FAQ
How are the steps shown?
The log shows each symbolic rule step (product, quotient, chain, and power). In numeric mode, it lists central difference and Richardson refinement in order.
Does it cover partial and implicit differentiation?
Yes. Partial mode reports ∂f/∂x and ∂f/∂y together. Implicit mode computes F_x and F_y, then reports dy/dx = -F_x/F_y with numeric values and tangent details.
Which differentiation mode should I choose first?
Choose symbolic mode for algebraic derivatives, numeric mode for a value-based check, tangent mode for a point on a curve, and implicit or partial mode when the expression is not a single y=f(x) function.
Why can another derivative tool show a different-looking answer?
Derivative tools can differ in simplification style, domain handling, numeric step size, and whether they display equivalent algebraic forms. Compare by substituting a test point into both derivatives.
When should I trust the symbolic result instead of the numeric derivative?
Symbolic results are exact when the parser supports the expression. Numeric derivatives are approximations, so check the step size and avoid points where the function is discontinuous or not differentiable.
Need integration steps too?
Use the Integration Calculator for numeric and basic symbolic integrals with step-by-step logs.
Differentiation workflow notes
Pick the derivative type
Use ordinary differentiation for y=f(x), partial derivatives for multivariable expressions, and implicit differentiation when x and y appear in the same equation.
Read steps before simplifying
The step log shows product, quotient, chain, and power rules before the final form. Equivalent simplified results may look different but describe the same derivative.
Numeric checks
Numeric differentiation is useful for verifying a value or tangent slope. It is less reliable near corners, discontinuities, vertical tangents, or very noisy expressions.
Common mistakes
Do not compare a derivative at a point with the whole derivative function. Do not forget parentheses around composite functions when testing chain-rule examples.
Using the result
For coursework, keep both the derivative expression and the rule sequence. For modeling, test the derivative at representative points before relying on the slope.