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ksaimouli
 2 years ago
derivative
ksaimouli
 2 years ago
derivative

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ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353885456771:dw

ivanmlerner
 2 years ago
Best ResponseYou've already chosen the best response.1You need to use the chain rule here. ln is one function, something^3 another and 12x another.

ivanmlerner
 2 years ago
Best ResponseYou've already chosen the best response.1Do you have any ideas on what the first step is?

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353887083835:dw

ivanmlerner
 2 years ago
Best ResponseYou've already chosen the best response.1Almost, you forgot to derivate the function z^3. You did the derivative of the ln and the one inside the cubic power.

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0so should i take derivative (12x)^3 i thought i should only take derivative of inside the ()^3

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353888159532:dw

ksaimouli
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353888193965:dw

ivanmlerner
 2 years ago
Best ResponseYou've already chosen the best response.1Now that is correct. Just to summarize you have the following:\[f(x)=\ln(x)\]\[g(x)=x^3\]\[h(x)=12x\]and you want\[\frac{df(g(h(x)))}{dx}=\frac{df}{dg}\frac{dg}{dh}\frac{dh}{dx}\]\[\frac{df}{dg}=\frac{1}{g}=\frac{1}{(12x)^3}\]\[\frac{dg}{dh}=3h^2=3(12x)^2\]\[\frac{dh}{dx}=2\]
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