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Let F(x)=f(x)g(x)h(x) for all real x, wh...

Let `F(x)=f(x)g(x)h(x)` for all real `x`, where `f(x),g(x)`, and `h(x)` are differentiable functions. At some point `x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0),` and `h^(prime)(x_0)=kh(x_0)`. Then k is________

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. True or False -The derivative of an even function is always an odd fun...

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  2. If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)) then (dy)/(dx)...

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  3. Let F(x)=f(x)g(x)h(x) for all real x, where f(x),g(x), and h(x) are di...

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  4. Find (dy)/(dx) for y=tan^(-1){(1-cosx)/(sinx)}.

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  5. If x=y+sin^2x then at x=0 ,(dy)/dx=

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  6. f(x)=sin^(-1)(2xsqrt(1-x^2)) then f'(x)=

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  7. If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= for x>20

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  8. Find (dy)/(dx) for y=tan^(-1) sqrt(sec^2x/ (cosec^2x))

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  9. If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a)(sinx)^(tanx)(1+sec^2xlogsi...

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  10. If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)

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  11. Suppose that f(x) is a quadratic expresson positive for all real x If ...

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  12. If y=cos^(-1)x ,find (d^2y)/(dx^2).

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  13. If y^2=P(x), where P(x) is a polynomial of degree 3, then 2d/dx(y^3(d^...

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  14. If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(...

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  15. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of li...

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  16. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

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  17. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

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  18. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

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  19. If (x-a)^(2)+(y-b)^(2)=c^(2), for some c gt 0, prove that ([1+((dy)/...

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  20. if y=(x^2-1)^m , then the (2m)th differential coefficient of y is

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