Mathematics, 10.06.2021 14:20 nataliahenderso
Logarithmic differentiation of f' when y=(Inx)^cosx (x>1)
Answers: 2
![\frac{dy}{dx} = (lnx)^{cosx } \cdot [\frac{cosx }{ln x} \cdot \frac{1}{x} - sin x ( ln ( ln x)) ]](/tpl/images/1369/8244/baca4.png)
                ![[ taking \ logarithm \ on \ both \ sides ]](/tpl/images/1369/8244/54425.png)
       ![[Chain rule : uv = u \frac{dv}{dx} + v \frac{du}{dv} ]](/tpl/images/1369/8244/788c5.png)
![\frac{dy}{dx} = y \times [\frac{cosx }{ln x} \cdot \frac{1}{x} - sin x ( ln ( ln x)) ]](/tpl/images/1369/8244/8e53d.png)
![[ substituting \ the \ value \ of \ y]](/tpl/images/1369/8244/32080.png)
  
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Logarithmic differentiation of f' when y=(Inx)^cosx (x>1)...
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