Differentiation C3 question Watch

ap121
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Differentiate:

y=ln(cosx)^2

This is the link for the worked solution given(question 11c) but it's confusing me.

https://www.activeteachonline.com/de...l/0/uid/357726

If we let u=cosx, then y=ln(u)^2

But the worked solution says y=lnu^2, which is different. It's similar to how ln(2)^2 is not the same as ln4. Can someone explain if I'm making a mistake? Because if y=ln(u)^2, you can't use the power rule to say y=2ln(u).
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Notnek
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(Original post by ap121)
Differentiate:

y=ln(cosx)^2

This is the link for the worked solution given(question 11c) but it's confusing me.

https://www.activeteachonline.com/de...l/0/uid/357726

If we let u=cosx, then y=ln(u)^2

But the worked solution says y=lnu^2, which is different. It's similar to how ln(2)^2 is not the same as ln4. Can someone explain if I'm making a mistake? Because if y=ln(u)^2, you can't use the power rule to say y=2ln(u).
It's confusing notation but they mean

\ln((\cos x)^2)

and not

(\ln(\cos x))^2

It would be clearer in an exam.
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Sataris
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If we let u = cosx, then y = \ln (u^2), not (\ln (u))^2
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carl fringos!
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(Original post by ap121)
Differentiate:

y=ln(cosx)^2

This is the link for the worked solution given(question 11c) but it's confusing me.

https://www.activeteachonline.com/de...l/0/uid/357726

If we let u=cosx, then y=ln(u)^2

But the worked solution says y=lnu^2, which is different. It's similar to how ln(2)^2 is not the same as ln4. Can someone explain if I'm making a mistake? Because if y=ln(u)^2, you can't use the power rule to say y=2ln(u).
Hi,
Its not different for the first part the brackets around the cosx are needed so you know you are not squaring just the x.
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ap121
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(Original post by Notnek)
It's confusing notation but they mean

\ln((\cos x)^2)

and not

(\ln(\cos x))^2

It would be clearer in an exam.
Nice, thanks.
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carl fringos!
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(Original post by ap121)
Differentiate:

y=ln(cosx)^2

This is the link for the worked solution given(question 11c) but it's confusing me.

https://www.activeteachonline.com/de...l/0/uid/357726

If we let u=cosx, then y=ln(u)^2

But the worked solution says y=lnu^2, which is different. It's similar to how ln(2)^2 is not the same as ln4. Can someone explain if I'm making a mistake? Because if y=ln(u)^2, you can't use the power rule to say y=2ln(u).
To be honest i would not do it that way its much simpler to just differentiate the ln leaving the (cosx)^2 there then times that by 2cosx(-sinx)
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ap121
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(Original post by carl fringos!)
To be honest i would not do it that way its much simpler to just differentiate the ln leaving the (cosx)^2 there then times that by 2cosx(-sinx)
Yes that sounds much simpler
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