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y=x log whole root of sin(x^2+1) differentiate with respect to x

y=x log whole root of sin(x^2+1) differentiate with respect to x

Grade:11

1 Answers

pavithra Ayyanar
21 Points
6 years ago
 
Dfferentiate  y = x log\sqrt{sin(x^{2}+1)}
 
     =  xlog\left [ sin(x^{2}+1) \right ]^{\frac{1}{2}}
 
     = \frac{x}{2}logsin(x^{2}+1)
 
   \frac{dy}{dx}  =  \frac{1}{2}\left [ x\left ( \frac{1}{sin(x^{2}+1)}cos(x^{2}+1)2x \right )+logsin(x^{2}+1) \right ]
 
Answer    dy/dx = x^{2}cot(x^{2}+1)+\frac{logsin(x^{2}+1)}{2}
 
Product rule = U dv/dx +V du/dx
 u = x
v = logsin(x2+1)
du/dx = 1
dv/dx = 1/sin(x2+1). cos(x2+1). 2x
 
 

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