Answer:
[tex]\frac{dy}{dx}=\frac{8lnx}{x}[/tex]
Step-by-step explanation:
We are given that a function
[tex]y=(lnx^2)^2[/tex]
We have to find the derivative of the function
Differentiate w.r.t x
[tex]\frac{dy}{dx}=2(lnx^2)\times \frac{1}{x^2}\times 2x[/tex]
By using formula
[tex]\frac{d(lnx)}{dx}=\frac{1}{x}[/tex]
[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]
[tex]\frac{dy}{dx}=\frac{4lnx^2}{x}=\frac{4(2)lnx}{x}[/tex]
by using [tex]lnx^y=ylnx[/tex]
Hence, the derivative of function
[tex]\frac{dy}{dx}==\frac{8lnx}{x}[/tex]
Answer: The required derivative is [tex]\dfrac{dy}{dx}=\\dfrac{4}{x\ln x^2}[/tex]
Step-by-step explanation:
Since we have given that
[tex]y=(\ln x^2)^2[/tex]
We need to derivative it w.r.t 'x'., using "Chain rule"
As we know that
[tex]\dfrac{d}{dx} \ln x=\dfrac{1}{x}\\\\and\\\\\dfrac{d}{dx}x^n=nx^{n-1}[/tex]
So, it becomes,
[tex]\dfrac{dy}{dx}=\dfrac{1}{\ln (x^2)^2}\times 2\ln(x^2)\times \dfrac{1}{x^2}\times 2x\\\\\dfrac{dy}{dx}=\dfrac{4}{x\ln x^2}[/tex]
Hence, the required derivative is [tex]\dfrac{dy}{dx}=\\dfrac{4}{x\ln x^2}[/tex]
