1. ## Derivatives: Logarithmic Differentiation

So i solved a few of the steps but i'm stuck at this one step and can't move on

Find y if

y=(10x+9)^10x+1

Note: The product of two numbers or two expressions should be entered as a*b. For the quotient of two numbers use a/b. For the power use a^b.

1. Take the natural logarithm of both sides:
lny = ln (10*x+9)^(10*x+1)

2. Simplify by using properties of logarithms:
lny = (10*x+1)*log(10*x+9)

3. Differentiate both sides with respect to x:

4. Solve for y:
y = y( )

5. Substitute the original expression for y to get y in terms of x only:
y =

If someone could help me from 3 onwards i would really appreciate it.

Thanks

2. can't you use $\frac{d(uv)}{dx}=\frac{du}{dx}.v+\frac{dv}{dx}.u$

then $y'y =(10x+1) \frac{10}{(10x+9)} + 10ln(10x+9)$

3. Ah that was it, thanks a lot!