# Thread: finding derivative

1. ## finding derivative

I have no idea what to do with this. I started with log differentiation but ran into a problem when dealing with the arcsin(7^x)

y=[arcsin(7^x)]^x

Lny = xLn[arcsin(7^x)] = x (1/arcsin(7^x)) * d/dx (arcsin(7^x)) ?

2. Originally Posted by bgonzal8
I have no idea what to do with this. I started with log differentiation but ran into a problem when dealing with the arcsin(7^x)

y=[arcsin(7^x)]^x

Lny = xLn[arcsin(7^x)] = x (1/arcsin(7^x)) * d/dx (arcsin(7^x)) ?
$\frac{d}{dx}\arcsin{7^x}=\frac{1}{\sqrt{1-(7^x)^2}}\cdot\frac{d}{dx}[7^x]$

3. Oh yeah duh.. then d/dx [a^x] = a^x Ln (a)

So is this right?
y = [arcsin(7^x)]^x * [(x/arcsin(7^x))] * [(7^xLn(7))/sqrt(1-(7^x)^2)]

4. Originally Posted by bgonzal8
Oh yeah duh.. then d/dx [a^x] = a^x Ln (a)

So is this right?
y = [arcsin(7^x)]^x * [(x/arcsin(7^x))] * [(7^xLn(7))/sqrt(1-(7^x)^2)]

Don't forget that you are using logarithmic differentiation.