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Is there some easy way where i only have to remember a few of them, and i can just figure out the rest from that?

thanks

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- Thread starter Physics is Phun
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- #1

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Is there some easy way where i only have to remember a few of them, and i can just figure out the rest from that?

thanks

- #2

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You don't need to memorize them. If you know the derivatives of sine and cosine, then you can get everything else from the product or quotient rules. For the inverses, either use the inverse rule for derivatives or do something like this:Physics is Phun said:

Is there some easy way where i only have to remember a few of them, and i can just figure out the rest from that?

thanks

[tex]\frac{d}{d\theta}\tan\left(\arctan{\theta}\right)=1[/tex]

[tex]\frac{d}{d\theta}\arctan{\theta}=\frac{1}{\sec^2\left(\arctan{\theta}\right)}[/tex]

Now use that identity tan

Chain rule will be useful for inverses, prod./quotient rules will be useful for others.

- #3

CarlB

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My latest favorite method of remembering the trig derivatives is this:

[tex]\frac{d}{dx}e^{ix} = i e^{ix} = e^{ix + \pi/2}[/tex]

From this, by taking real and imaginary parts you get:

[tex]\frac{d}{dx}\sin(x) = \sin(x+\pi/2)[/tex]

[tex]\frac{d}{dx}\cos(x) = \cos(x+\pi/2)[/tex]

The derivatives of the trig functions are changes to the phase. You can use trig rules to get the usual forms:

[tex]\sin(x+\pi/2) = \sin(\pi/2)\cos(x)+ \cos(\pi/2)\sin(x) = \cos(x)[/tex]

[tex]\cos(x+\pi/2) = \cos(\pi/2)\cos(x)-\sin(\pi/2)\sin(x) = -\sin(x)[/tex]

And always remember, the exponential function is your buddy.

Carl

[tex]\frac{d}{dx}e^{ix} = i e^{ix} = e^{ix + \pi/2}[/tex]

From this, by taking real and imaginary parts you get:

[tex]\frac{d}{dx}\sin(x) = \sin(x+\pi/2)[/tex]

[tex]\frac{d}{dx}\cos(x) = \cos(x+\pi/2)[/tex]

The derivatives of the trig functions are changes to the phase. You can use trig rules to get the usual forms:

[tex]\sin(x+\pi/2) = \sin(\pi/2)\cos(x)+ \cos(\pi/2)\sin(x) = \cos(x)[/tex]

[tex]\cos(x+\pi/2) = \cos(\pi/2)\cos(x)-\sin(\pi/2)\sin(x) = -\sin(x)[/tex]

And always remember, the exponential function is your buddy.

Carl

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