Enter f(x) and g(x) in one line easily. Get derivative, steps, and sample table instantly. Download a report, share data, and verify values today.
sin(x), cos(x), tan(x), exp(x), ln(x), log(x), sqrt(x), abs(x). Use ^ for powers and * for multiplication.
This tool differentiates f and g symbolically, then combines them using the product rule.
| f(x) | g(x) | x | Expected (f·g)' |
|---|---|---|---|
| x^2 | sin(x) | 1 | 2x·sin(x) + x^2·cos(x) |
| exp(x) | x^3 | 0 | exp(x)·x^3 + exp(x)·3x^2 |
| ln(x) | sqrt(x) | 4 | (1/x)·sqrt(x) + ln(x)·(1/(2sqrt(x))) |
These examples match the product rule structure used above.
It is a differentiation rule for a product of two functions. If h(x)=f(x)g(x), then h′(x)=f′(x)g(x)+f(x)g′(x). It prevents common mistakes from multiplying derivatives directly.
You can use +, −, *, /, ^, parentheses, and common functions like sin, cos, exp, ln, log, sqrt, and abs. Write multiplication explicitly with * to avoid ambiguity.
NaN usually appears when an expression is undefined at a chosen x value. Examples include ln(x) for x≤0, division by zero, or sqrt(x) for x<0. Try different evaluation points.
Yes. Enable “Show step-by-step explanation” to display the product-rule structure and how the derivatives are combined. The tool also prints f′(x), g′(x), and the final expanded form.
General power forms are rewritten using exp(v·ln(u)) before differentiating, which supports many cases. If the base becomes nonpositive at your evaluation points, ln(u) may be undefined and NaN can appear.
ln(x) is the natural logarithm (base e). log(x) here represents base-10 logarithm. Both require x>0 for real-valued results. Choose the one that matches your math context.
After a successful calculation, use the Download buttons. CSV exports the evaluation table for spreadsheets. PDF exports a clean text report with inputs, derivatives, the final expression, and the same table.
Pick several evaluation points and compare the table output with a manual check. You can also change precision to see rounding effects. If values look unstable, try points away from discontinuities or steep regions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.