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FP3 hyperbolic differentiation help

How do you differentiate -tanh(x)sech(x)? Whenever I do it (using the product rule) I get sech(x)tanh^2(x) - sech^3(x), but the answer in the Solution Bank is sech^3(x) - sech(x)tanh^2(x). I don't know if I'm making a stupid error somewhere, or if I'm using the wrong rule.

Will rep any answers that clear this up. Cheers
Reply 1
Avatar for Ayman!
Ayman!
15
Original post by ChrisP97
How do you differentiate -tanh(x)sech(x)? Whenever I do it (using the product rule) I get sech(x)tanh^2(x) - sech^3(x), but the answer in the Solution Bank is sech^3(x) - sech(x)tanh^2(x). I don't know if I'm making a stupid error somewhere, or if I'm using the wrong rule.

Will rep any answers that clear this up. Cheers


Your working is completely correct. Ignore the solution bank. I have just worked it out myself and I'm getting the same answer as yours.
Original post by ChrisP97
How do you differentiate -tanh(x)sech(x)? Whenever I do it (using the product rule) I get sech(x)tanh^2(x) - sech^3(x), but the answer in the Solution Bank is sech^3(x) - sech(x)tanh^2(x). I don't know if I'm making a stupid error somewhere, or if I'm using the wrong rule.

Will rep any answers that clear this up. Cheers


Differential of sech(x) = -sech(x)tanh(x) can prove this by the quotient rule (remember unlike in trig, diff of cosh = sinh, not -sinh. Differential of -tanh(x) = -sech^2 (x), then just apply the product rule and bingo
Reply 3
Avatar for Ayman!
Ayman!
15
Original post by MathsAstronomy12
Differential of sech(x) = -sech(x)tanh(x) can prove this by the quotient rule (remember unlike in trig, diff of cosh = sinh, not -sinh. Differential of -tanh(x) = -sech^2 (x), then just apply the product rule and bingo


I believe it's derivative and not differential?
Original post by aymanzayedmannan
I believe it's derivative and not differential?


Yeh my bad haha
Original post by aymanzayedmannan
Your working is completely correct. Ignore the solution bank. I have just worked it out myself and I'm getting the same answer as yours.


Original post by MathsAstronomy12
Differential of sech(x) = -sech(x)tanh(x) can prove this by the quotient rule (remember unlike in trig, diff of cosh = sinh, not -sinh. Differential of -tanh(x) = -sech^2 (x), then just apply the product rule and bingo


Ok great thanks, at least I'm doing it correct. I wish Edexcel would bother checking the resources they publish instead of leaving it to students to find the mistakes :/
Reply 6
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TeeEm
19
Original post by ChrisP97
leaving it to students to find the mistakes :/


you learn better that way ,,,
c22.jpg61.3KB
Reply 7
Avatar for Ayman!
Ayman!
15
Original post by ChrisP97
Ok great thanks, at least I'm doing it correct. I wish Edexcel would bother checking the resources they publish instead of leaving it to students to find the mistakes :/


The FP2 book has some pretty bad ones. I won't even get into the M2 book.
Original post by ChrisP97
Ok great thanks, at least I'm doing it correct. I wish Edexcel would bother checking the resources they publish instead of leaving it to students to find the mistakes :/


I don't think the Solution Bank is made by Edexcel (that is if we are talking about the same one).

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