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If y=(log)a x , find (dy)/(dx) ....

If `y=(log)_a x` , find `(dy)/(dx)` .

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To find the derivative of \( y = \log_a x \), we will follow these steps: ### Step 1: Change of Base Formula We use the change of base formula for logarithms, which states: \[ \log_a x = \frac{\log_e x}{\log_e a} \] This allows us to express the logarithm in terms of natural logarithms (base \( e \)). ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=x^x , find (dy)/(dx) at x=e .

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  2. If y=tan^(-1)((1-x)/(1+x)) , find (dy)/(dx) .

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  3. If y=(log)a x , find (dy)/(dx) .

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  4. If y=logsqrt(tanx) , write (dy)/(dx) .

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  5. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

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  6. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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  7. If |x|<1 and y=1+x+x^2+....... oo , then find the value of (dy)/(dx)...

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  8. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1 < ...

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  9. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  10. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

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  11. If f(x) is an even function, then write whether f^(prime)(x) is eve...

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  12. If f(x) is an odd function, then write whether f^(prime)(x) is even...

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  13. Write the derivative of sinx with respect to cosx .

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  14. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

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  15. The differential coefficient of f(logx) with respect to x , where f(...

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  16. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 i...

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  17. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

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  18. If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx) at ...

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  19. If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+1/x)^x{log(1+1/x)-1/(x+1)} (b)...

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  20. If x^y=e^(x-y) , then (dy)/(dx) is (a)(1+x)/(1+logx) (b) (1-logx)/(1+l...

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