Differentiation using quotient rule: Can somebody please tell me how to solve this red arrow part, see the attached image file
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OpenStudy (anonymous):
OpenStudy (anonymous):
8-12=-4, so you have -4x^2
That part is just algebra
OpenStudy (anonymous):
No, I meant to say where we got that 8^4 +24x part
OpenStudy (experimentx):
8x^3*x
from previous step
OpenStudy (anonymous):
yes but how, can you please explain it ..
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OpenStudy (anonymous):
(x * y') - (x' * y) / (x)^2
OpenStudy (experimentx):
Simplify this
\[ \frac{(x^3 + 3)8x - 4x^2 (3x^2)}{(x^3+2)^2}\]
OpenStudy (anonymous):
(3x^3+8x-4x^2) / (x^3+2)^2
OpenStudy (anonymous):
oh sorry, I didn't see the power signs are too small ..
(x^3+3 +8x) - (12x^2) / (x^3+3)^2
OpenStudy (anonymous):
When you simplify it you will get the final answer shown below the red arrow.
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OpenStudy (anonymous):
yes, I am not good at simplifying. I almost forgot it.
OpenStudy (experimentx):
your steps are incorrect!!
how can you be doing calculus ... ?? i think you should start with basic algebra
OpenStudy (anonymous):
Let try basic algebra :
(x³+3) 8x = ...
OpenStudy (anonymous):
can you please mention a link or tutorial where I can learn simplification and algebra. I don't think I am able to do derivative unless I learn some basic algebra.
OpenStudy (anonymous):
Can distribute ( multiply) 8x into the parentheses ?
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OpenStudy (anonymous):
you?
OpenStudy (anonymous):
8x^3+3 ?
OpenStudy (anonymous):
How about: 8x * x³ = ..
OpenStudy (anonymous):
24x^3 ?
OpenStudy (anonymous):
Add exponents when you multiply
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OpenStudy (anonymous):
or it could be 8x and add powers? = 8x^4 ?
OpenStudy (anonymous):
Don't get confused between exponent and the constant:
OpenStudy (anonymous):
Yep, 8x^4 ( sigh !)
OpenStudy (anonymous):
3* 8x = ?
OpenStudy (anonymous):
24x , right?
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OpenStudy (anonymous):
Yep, now (x³+3) 8x = ...
OpenStudy (anonymous):
8x^4 + 24x
OpenStudy (anonymous):
and in the last part .. 4*3 = 12 ... then add exponents 12x^4
OpenStudy (anonymous):
Great :)
4x² * 3x² =
OpenStudy (anonymous):
Good job, now put them together!
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OpenStudy (anonymous):
Thank you so much @Chlorophyll .. Can you please give me a tutorial link where I can do exercises of simplifcations?