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Differentiate x^2cosx...

Differentiate `x^2cosx`

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To differentiate the function \( f(x) = x^2 \cos x \) using the first principle of derivatives, we will follow these steps: ### Step 1: Write the definition of the derivative The derivative of a function \( f(x) \) from the first principle is given by: \[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \] ...
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RD SHARMA-DERIVATIVES-Solved Examples And Exercises
  1. If y=sqrt(x/a)+sqrt(a/x) , prove that 2x y(dy)/(dx)=(x/a-a/x)

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  2. If for f(x)=lamdax^2+mux+12 and f'(4)=15 and f'(2)=11, then find lamda...

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  3. Differentiate x^2cosx

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  4. Using first principles, prove that d/(dx){1/(f(x))}=-(f^(prime)(x))/({...

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  5. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

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  6. The differentiation of loge x ,i s1/xdot i.e. d/(dx)((loge x)=1/x)

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  7. Differentiate the following functions with respect to x from first...

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  8. Differentiate x^n by first princeple

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  9. Differentiate the following functions with respect to x from first p...

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  10. The differentiation of t a nx with respect to x is sec^2xdot i.e. d/(...

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  11. The differentiation of cotx with respect to x is-cos e c^2xdot i.e. ...

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  12. (x) The differentiation of secx with respect to x is secxtanx

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  13. The differentiation of cos e cx with respect to xis -c o s e cxcotxdot...

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  14. The differentiation of e^-x with respect to x is -e^-xdot i.e. d/(dx)...

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  15. Differentiate the following functions with respect to x : e^(3logx...

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  16. Let f(x) be a differentiable and let c a be a constant. Then cf(x) is ...

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  17. Differentiate the following functions with respect to x : (sqrt(x...

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  18. Differentiate the following functions with respect to x : (3^x)/(x+t...

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  19. Differentiate the following functions with respect to x : (10^x)/(s...

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  20. f(x)=x^2e^xlogx differentiate f(x) with respect to x at x = 1

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