• Math Doubts
• Differential calculus
• Differentiation
• Rules

There are six derivative rules to evaluate the differentiation of the hyperbolic functions in differential calculus. So, learn every derivative formula of hyperbolic functions with mathematical proofs.

Hyperbolic sine function

$\dfrac{d}{dx}{\,\sinh{x}} \,=\, \cosh{x}$

Hyperbolic Cosine function

$\dfrac{d}{dx}{\,\cosh{x}} \,=\, \sinh{x}$

Hyperbolic Tan function

$\dfrac{d}{dx}{\,\tanh{x}} \,=\, \operatorname{sech}^2{x}$

Hyperbolic Cot function

$\dfrac{d}{dx}{\,\coth{x}} \,=\, -\operatorname{csch}^2{x}$

Hyperbolic Secant function

$\dfrac{d}{dx}{\,\operatorname{sech}{x}} \,=\, -\operatorname{sech}{x}\tanh{x}$

Hyperbolic Cosecant function

$\dfrac{d}{dx}{\,\operatorname{csch}{x}} \,=\, -\operatorname{csch}{x}\coth{x}$

Ashok Kumar, B.E.

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A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

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