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lgg23
 4 years ago
Find the derivative of f(x)=8(x^4) arctan (9x^3)
lgg23
 4 years ago
Find the derivative of f(x)=8(x^4) arctan (9x^3)

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lgg23
 4 years ago
Best ResponseYou've already chosen the best response.0I think I'm making minor mistakes...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[8x ^{4}\times \tan^{1} (9x ^{3}) = 32x ^{3}\times \tan^{1} (9x ^{3}) + 8x ^{4}\times(27x ^{2}/(1+81x ^{6}))\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0\[\text{ let } g=\arctan(9x^3) => \tan(g)=9x^3 =>g' \sec^2(g)=27x^2 \] \[=> g'=\frac{72 x^2}{\sec^2(g)}\] Now if tan(g)=9x^3/1=(opp/adj) Then assuming we have a right triangle the hyp is... \[hyp=\sqrt{(9x^3)^2+1^2}=\sqrt{81x^6+1}\] So we have \[g'=\frac{72x^2}{(\sqrt{81x^6+1})^2}=\frac{72x^2}{8x^6+1}\] so we have the derivative of f is... \[f'=32x^3 \arctan(9x^3)+8x^4 \frac{72x^2}{8x^6+1}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0oops 72 is suppose to be 27 lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0and 8 is suppose to be 81

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes :), @myiniaya one question, how i can write the line of division :/

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1328491764888:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{thank}{you}\] ok :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@igg23 , remember : \[f(x)=\arctan(u)\] then \[f \prime(x)=\frac{u \prime}{1+u ^{2}}\]
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