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Differentiate the function with respect ...

Differentiate the function with respect to `x` using the first principle : `(log)_e x`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
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  2. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x)...

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  3. Differentiate the function with respect to x using the first principle...

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  4. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2)= (a)3/2 (b) 3/((4t)) (c) 3/(2...

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  5. Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...

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  6. If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e...

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  7. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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  8. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

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  9. If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

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  10. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

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

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  12. If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+...

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  13. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...

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  14. Let y=1n(1+cosx)^2. Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal

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  15. Find (dy)/(dx)"for"y=xsinxlogxdot

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  16. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

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  17. Differentiate y=(e^x)/(1+sinx)

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  18. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

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  19. If y=sqrt((1-x)/(1+x)), prove that (1-x^2)dy/(dx)+y=0

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  20. If g(x)=(f(x))/((x-a)(x-b)(x-c)),where f(x) is a polynomial of degree ...

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