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# Quick differentiation question Watch

1. Trying to differentiate:

1/cosh(x)

I know what it should end up as:

-sinh(x) / cosh^2(x)

but I don't know how to get to it.

Thanks.
2. (Original post by mackemforever)
Trying to integrate:

1/cosh(x)

I know what it should end up as:

-sinh(x) / cosh^2(x)

but I don't know how to get to it.

Thanks.
That's the derivative of 1/cosh(x) and not the integral.
To evaluate this integral rewrite it as:

.

Then use a substitution of if you can't spot by inspection that this integral leads to arctan.

3. let

you should then be able to rearrange and get it to

which is a standard integral
4. (Original post by mackemforever)
Trying to integrate:

1/cosh(x)

I know what it should end up as:

-sinh(x) / cosh^2(x)

but I don't know how to get to it.

Thanks.
To solve
where R is a fuction formed with rational operations from
the given functions and constans, use the substittion of
5. Crap, sorry, I meant differentiate!

6. (Original post by mackemforever)
Crap, sorry, I meant differentiate!

In which case, you should use the chain rule.
i.e. note that:
.
Now if you let then and our original derivative becomes . Then note that

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