help with easy derivative problem

[redd8937]

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I don't understand for the life of me why everytime there is a question such as

y = sin (2x^3-2) Find the derivative
I always think the answer should be:

cos(u) * u' where u= 2x^3-2

or

6x^2 cos (2x^3-2)

BUT whenever I put it in a derivative program online it always switches what's in the parentheses and makes the answer:

6x^2 cos (2-2x^3)

I have no idea why it switched and the first step in these online programs that work it out are always rewriting the equation

so the original equation of
y = sin (2x^3-2) becomes -sin(2-2x^3)

why does it do that!? I'm so confused

 

[fullmetalphrm]

Because apparently it's a faulty online calculator I suppose.

In your example 6x^2*cos(2x^3-2) is the right answer. I popped it into this calculator and got the same thing: http://www.numberempire.com/derivatives.php

So don't get too hung up on it, you can apparently do basic derivatives which is what most of the PCAT calc based questions are based on. Good luck.👍

 

[gsw650]

your answer is correct. I don't know what's wrong with the program you're using but try these instead:
http://www.mycalculus.com/calculus_solver.aspx
http://www.wolframalpha.com/

 

[redd8937]

your answer is correct. I don't know what's wrong with the program you're using but try these instead:
http://www.mycalculus.com/calculus_solver.aspx
http://www.wolframalpha.com/

the wolframalpha link gives me the other answer too, i don't get it!

 

[redd8937]

the wolframalpha link gives me the other answer too, i don't get it!

I think i got it.

cos(5-4) = cos(4-5)

the order doesn't matter, just some websites use a different notation. i didn't realize cos(this # is just computed as an absolute value) because cos(-200)=cos(200)

 

[xraynova]

The cosine function is an even function and the sine function is an odd function. That means, cos (+x) = cos(-x) and sin(-x) = -sin(+x). Look at it graphically. If you plot the cosine function from, say, -2*Pi to +2*Pi, you can perfectly fold the graph along the y axis and the negative x-axis part of the curve falls precisely onto the positive x-axis part. On the other hand, the sine curve plotted from -2*Pi to +2*Pi will not reflect across the y-axis. Therefore, both answers posted by REDD8937 are correct.