find the derivative of y=log10(5x^4-2/x^3)

Question

anonymous · Answer

this involves both the chain rule and the quotient rule

mimi_x3 · Answer

or you can use log laws to change it first; then diferentiate it, would be easier.

anonymous · Answer

@failmathmajor only the 2/x^3 is a fraction

mimi_x3 · Answer

is it
$$\log\left(5x^{4}-\frac{2}{x^{3}}\right)  ?$$

anonymous · Answer

that would be much easier

anonymous · Answer

so using log properties you can say that $$\log_{10} {x} = \ln x / \ln 10 $$

anonymous · Answer

ln10 is a constant, you can factor that out

anonymous · Answer

can you use the chain rule fluently?

anonymous · Answer

y'=pu(x) * u'(x) right?

anonymous · Answer

d(f(g(x))/dx = (dg(x)/dx)*(df(g(x))/dx) is the way I know it

mimi_x3 · Answer

Or..$$y= \log\left(5x^{4}-\frac{2}{x^{3}}\right)   y = \log\left(\frac{5x^{7}-2}{x^{3}}\right)   => y = \log\left(5x^{7}-2\right)   - \log(x^3)$$
Might be easier; than the quotient role and chain rule..

anonymous · Answer

that may look confusing now that I see it

anonymous · Answer

don't need the quotient in this case:
can treat /x^3 as a x^-3

mimi_x3 · Answer

@cunninnc: are you able to do it now?

anonymous · Answer

and you would still need the chain rule for that anyway

anonymous · Answer

but enough arguing

mimi_x3 · Answer

Did an argument started? lol

anonymous · Answer

$$(d(\ln (5x^4 - 2x^{-3}))/dx )/ \ln10$$
is what it simplifies down to, to be concise

anonymous · Answer

@Mimi_x3  kinda .... i see mr. moose got 2x^-3  where does ^-3 come froms

anonymous · Answer

$$2/x^3= 2 * x^{-3}$$

mimi_x3 · Answer

Sorry i don't know what MrMoose is doing. 
@MrMoose: Use \frac{x}{y} for fractions :)

mimi_x3 · Answer

Or why not try the method that i used :)
$$ \frac{d}{dx}  \log\left(5x^{7}-2\right)   -\frac{d}{dx}   \log(x^3)$$

anonymous · Answer

when you divide you subtract exponents, so that is equivalent to saying $$2 * \frac{x^0}{x^3}$$
then subtract exponents in division

anonymous · Answer

$$\frac{\frac{d(\ln(5x^4−2x^{−3}))}{dx}}{\ln10}$$

anonymous · Answer

@catamountz15 
what?

anonymous · Answer

I am almost entirely sure that that isn't a form of the answer.

anonymous · Answer

Here are the steps in to solving this problem.

anonymous · Answer

that isn't what you wrote though

anonymous · Answer

My apologies that was an answer to a different problem.