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Find second order derivative of x^3lo...

Find second order derivative of `x^3logx`

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To find the second order derivative of the function \( f(x) = x^3 \log x \), we will follow these steps: ### Step 1: Find the first derivative \( f'(x) \) We will use the product rule for differentiation, which states that if we have two functions \( u(x) \) and \( v(x) \), then the derivative is given by: \[ (uv)' = u'v + uv' ...
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. Find second order derivative of e^xsin5x

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  2. Find second order derivative of e^(6x)cos3x

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  3. Find second order derivative of x^3logx

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  4. Find second order derivative of tan^(-1)x

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  5. Find second order derivative of xcosx

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  6. Find second order derivative of log(logx)

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  7. If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

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  8. If y=x+tanx , show that cos^2x\ (d^2y)/(dx^2)-2y+2x=0 .

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  9. If y=x^3logx , prove that (d^4y)/(dx^4)=6/x .

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  10. If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

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  11. If y=2sinx+3cosx , show that (d^2y)/(dx^2)+y=0 .

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  12. If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .

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  13. If x=asectheta , y=btantheta , prove that (d^2y)/(dx^2)=-(b^4)/(a^2\ y...

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  14. If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove t...

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  15. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

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  16. If x=acostheta , y=bsintheta , show that (d^2y)/(dx^2)=-(b^4)/(a^2y^3)...

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  17. If x=a(1-cos^3theta) , y=a\ s in^3theta , prove that (d^2y)/(dx^2)=(32...

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  18. If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a...

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  19. If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

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  20. If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1...

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