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"If "y=(root(3)(1+3x)root(4)(1+4x)root(5...

`"If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)(1+8x)),` then y'(0) is equal to -

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`y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)(1+8x))`
`log_(e)y=(1)/(3)log_(e)(1+3x)+(1)/(4)log_(e)(1+4x)+(1)/(5)log_(e)(1+5x)-(1)/(7)log_(e)(1+7x)-(1)/(8)log_(e)(1+8x)`
Differentiating w.r.t. x
`(1)/(y)xx(dy)/(dx)=(1)/(1+3x)+(1)/(1+4x)+(1)/(1+5x)-(1)/(1+5x)-(1)/(1+7x)-(1)/(8x)`
`"At "x=0, y=1`
`rArr" "((dy)/(dx))_(x=0)=1+1+1-1-1=1`
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CENGAGE-DIFFERENTIATION-Exercise (Numerical)
  1. "Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the v...

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  2. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

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  3. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

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  4. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

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  5. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  6. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) then c is equal to

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  7. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

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  8. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

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  9. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

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  10. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

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  11. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  12. lim(hrarr0) ((e+h)^(In(e+h))-e)/(h) is-

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

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  15. A nonzero polynomial with real coefficients has the property that f(x)...

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  16. A function is reprersented parametrically by the equations x=(1+t)/(t^...

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  17. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

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  18. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  19. Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Compute the value of f(50)dotf^(p...

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  20. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

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