Question

what is the derivative of log 5 sqrt 5x+2

Answer 1

Log base 5, or base 10?

Answer 2

5

Answer 3

Ok hang on.

Answer 4

I was thinking 1/ln5 * (5/2sqrt5x+2)
now I'm stuck

Answer 5

So maybe it is dy/dx= 5/(ln5)(5x+2)

Answer 6

Ok let u equal sqrt(5x+2). So we have.
\[\log_{5}u \]
The derivative is then
\[\frac{ 1 }{ u \ln 5 }\]
In this case 'u' is \[\sqrt{5x+2}\]
So we have
\[\frac{ 1 }{ \sqrt{5x+2}\ln5 }\]

Answer 7

Now by the definition of the chain rule we have to multiply by the derivative of
\[\sqrt{5x+2}\]
and that is
\[\frac{ 5 }{ 2\sqrt(5x+2) }\]

Answer 8

I like where this is going...I think I am on track

Answer 9

So now it's
\[\frac{ 1 }{ \ln5\sqrt(5x+2) } * \frac{ 5 }{ 2\sqrt(5x+2) }\]
and that is
\[\frac{ 5 }{ \ln5(10x+4) }\]

You might have to check that though.

Answer 10

Sorry, online class so I am teaching myself from the book basically. Why did you multiply?

Answer 11

O gosh, wow...wow that was stupid. I see

Answer 12

So the chain rule is

The derivative of f(g(x)) is
f'(g(x))*g'(x)

In this case f(x) is log 5 x
and g(x) is sqrt(5x+2)
The annoying part is that you have to apply the chain rule again to
sqrt(5x+2)

Answer 13

Alright, sweet

Answer 14

Thanks so much :)

Answer 15

np!