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Differentiating functions of x with respect to x

If I'm given the following formulas

x=2e^2y

and

x=ln(2y+3)

How would I differentiate them with respect to x?
Original post by zoeedwards8
If I'm given the following formulas

x=2e^2y

and

x=ln(2y+3)

How would I differentiate them with respect to x?

Use chain rule.
Original post by zoeedwards8
If I'm given the following formulas

x=2e^2y

and

x=ln(2y+3)

How would I differentiate them with respect to x?


Bro whats y equal to ?
Reply 3
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math42
20
Original post by zoeedwards8
If I'm given the following formulas

x=2e^2y

and

x=ln(2y+3)

How would I differentiate them with respect to x?


Well you need to know the general differentials of exponentials and logs and you need to use the chain rule. Do you have an idea of what to do for either of them or do you need info on any of those things?
Reply 4
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zoeedwards8
OP
Original post by Duke Glacia
Bro whats y equal to ?


That's why I'm confused? All the other questions I have are y=x functions but both of these questions are x equations and it asks me to find the differentiation in terms of x
Reply 5
Avatar for zoeedwards8
zoeedwards8
OP
Original post by 1 8 13 20 42
Well you need to know the general differentials of exponentials and logs and you need to use the chain rule. Do you have an idea of what to do for either of them or do you need info on any of those things?


I know the rules it's just I'm not sure how to apply them. Like in question b I know that if x=lna then a=e^x but idk what to do
Original post by zoeedwards8
That's why I'm confused? All the other questions I have are y=x functions but both of these questions are x equations and it asks me to find the differentiation in terms of x
This is eactly what the chain rule lets you do:

ddxf(y(x))=dydxdfdy\dfrac{d}{dx} f(y(x)) = \dfrac{dy}{dx} \dfrac{df}{dy}


e.g.

ddxsin⁡y=dydxcos⁡y\dfrac{d}{dx} \sin y = \dfrac{dy}{dx} \cos y
(edited 8 years ago)
Original post by zoeedwards8
That's why I'm confused? All the other questions I have are y=x functions but both of these questions are x equations and it asks me to find the differentiation in terms of x


havent you learnt logarithms ? I think rearraging that isnt that hard. Or you can find dx/dy and take the reciprocal of it
To find dy/dx, find dx/dy and then find 1 / (dx/dy)
Reply 9
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zoeedwards8
OP
So for the first question the answer would be 1/4e^2y?
Original post by zoeedwards8
So for the first question the answer would be 1/4e^2y?


Yep you've got it!
Reply 11
Avatar for zoeedwards8
zoeedwards8
OP
Original post by CleverGirl383
Yep you've got it!


And would the second answer be 2y+3 all over 2?
Original post by zoeedwards8
And would the second answer be 2y+3 all over 2?



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