Differentiate : 2x * log10(x^1/2)

Question

Differentiate : 2x * log₁₀(√x)

#21, p223

Answer 1

I am assuming this is log base 10 right?

 

The way I tell my students to do this is to change the base. 

 

Basically log of x = (ln x)/ln(10)

 

So this would be 2x * ln (x^1/2)/ln(10)

 

What you can do here is the product rule with quotient rule

 

1st d 2nd + 2nd d 1st

 

2x * (ln(10)*1/x^1/2)*1/2x^-1/2 -ln x (0))/(ln(10))² + ln(x)/ln(10) * 2

 

You can then simplify it as necessary....