Question

differentiation Of cosh ax​

Answer 1

(sinhx)′=(ex−e−x2)′=ex+e−x2=coshx,(coshx)′=(ex+e−x2)′=ex−e−x2=sinhx. We can easily obtain the derivative formula for the hyperbolic tangent: (tanhx)′=(sinhxcoshx)′=(sinhx)′coshx−sinhx(coshx)′cosh2x=coshx⋅coshx−sinhx⋅sinhxcosh2x=cosh2x−sinh2xcosh2x.

Answer 2

Answer:

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(sinhx)′=(ex−e−x2)′=ex+e−x2=coshx,(coshx)′=(ex+e−x2)′=ex−e−x2=sinhx. We can easily obtain the derivative formula for the hyperbolic tangent: (tanhx)′=(sinhxcoshx)′=(sinhx)′coshx−sinhx(coshx)′cosh2x=coshx⋅coshx−sinhx⋅sinhxcosh2x=cosh2x−sinh2xcosh2x.