Compute sinh, cosh, tanh, sech, csch, coth derivatives. Use chain rules, evaluation, and export tools. Study identities, verify answers, and build stronger problem-solving confidence.
| Function | Input Form | Derivative | Point Check |
|---|---|---|---|
| sinh | 2·sinh(3x + 1) | 6·cosh(3x + 1) | x = 0 gives 9.258524345 |
| tanh | 4·tanh(2x - 1) | 8·sech²(2x - 1) | x = 1 gives 3.359437376 |
| sech | -3·sech(x + 2) | 3·sech(x + 2)·tanh(x + 2) | x = 0 gives 0.7676862813 |
The calculator uses y = a·f(bx + c). It applies the chain rule. The inner derivative is b. The outer multiplier is a.
For the full expression, multiply each result by a. That produces a·f′(u)·u′.
Hyperbolic functions appear in calculus, engineering, physics, and data modeling. Their derivatives follow clear patterns. This calculator helps students and professionals compute them quickly. It also explains the chain rule behind every answer.
The tool supports sinh, cosh, tanh, sech, csch, and coth. You can enter an outer multiplier, an inner coefficient, and an inner constant. That structure matches many textbook expressions. It also fits practical symbolic differentiation tasks.
After submission, the calculator returns the original function, the general derivative, and the derivative at a chosen point. This creates a full learning workflow. You can compare symbolic output with numeric evaluation. You can also export results for notes, assignments, or revision.
Hyperbolic derivatives are important because many models use exponential growth forms. The identities connect directly with exponentials. For example, sinh and cosh often appear in cable curves, heat transfer, and relativistic formulas. Tanh appears in signal processing and machine learning activation functions.
The chain rule is central here. When a hyperbolic function contains a linear inner expression, the derivative gains an extra factor from that inner term. This calculator applies that rule automatically. It reduces algebra mistakes and saves checking time.
Students often confuse trigonometric and hyperbolic derivatives. This page helps separate them. For instance, the derivative of sinh is cosh, while the derivative of cosh is sinh. The derivative of tanh becomes sech squared. Negative signs also matter for csch, sech, and coth.
Use the example table to understand expected inputs and outputs. Then test your own values. If a function becomes undefined at a chosen point, the calculator warns you. That is useful for csch and coth near zero.
This calculator is useful for homework practice, exam review, and concept reinforcement. It gives structured outputs, export options, and formula notes. That makes it a practical derivative reference for everyday calculus study.
Because the output is organized clearly, you can trace each transformation step. That makes the calculator suitable for self-study and classroom demonstration. Clear notation improves retention. Repeated practice with evaluated points also strengthens intuition about growth, symmetry, and function behavior across different real-number inputs in advanced calculus settings. It also supports neat records for later review.
It differentiates sinh, cosh, tanh, sech, csch, and coth expressions. It also handles an outer multiplier and a linear inner expression using the chain rule.
Yes. The result section shows the original function, the symbolic derivative, and the main chain rule steps. That makes it useful for learning and checking manual work.
Yes. Enter a value for x and the calculator will compute the derivative numerically. Leave the x field empty if you only want the general derivative formula.
Both functions depend on sinh(u) in the denominator. When sinh(u) equals zero, the real-number value is undefined. The calculator warns you when that happens during point evaluation.
Yes. The calculator multiplies the base derivative by the inner derivative and the outer coefficient. This is important when the input has the form a·f(bx + c).
Yes. After calculating, use the CSV button for spreadsheet data or the PDF button for a formatted summary. This helps with revision, reporting, and saved examples.
Use real numbers for the outer multiplier, inner coefficient, inner constant, and optional x value. The tool is designed for expressions built from a linear inner term.
Students, teachers, engineers, and anyone reviewing calculus can use it. It is especially helpful for practice problems, homework checking, and quick derivative verification.
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.