Question

derivative of complex fcn

Answer 1

\[y=2x \log_{10}\sqrt{x}\] find \[y'\]

Answer 2

product rule for this one
the derivative of \(2x\) is \(2\) and the derivative of \(\log_{10}(x)\) is \(\frac{1}{x\ln(10)}\)

Answer 3

whoa you have \(\log(\sqrt{x})\) wasn't paying attention.
no matter, start by writing \(\log(\sqrt{x})=\frac{1}{2}\log(x)\) an differentiate
\[x\log(x)\] again using the produce rule

Answer 4

use \((fg)'=f'g+g'f\) with \(f(x)=x, f'(x)=1,g(x)=\log(x), g'(x)=\frac{1}{x\ln(10)}\)

Answer 5

shouldnt this be chain rule?

Answer 6

i think here, it doesnt need chain rule but product rule
satellite is right

Answer 7

how is \[\log_{10}(\sqrt{x})=\frac{ 1 }{ 2 } \log_{10} x\] ?

Answer 8

because :

Answer 9

and we use property of logarithm :