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

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 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 the value of k is

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To solve the problem, we start with the function \( F(x) = f(x) g(x) h(x) \) and differentiate it using the product rule. ### Step-by-Step Solution: 1. **Differentiate \( F(x) \)**: We apply the product rule for differentiation: \[ F'(x) = f'(x) g(x) h(x) + f(x) g'(x) h(x) + f(x) g(x) h'(x) ...
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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 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 ENGLISH-DIFFERENTIATION-Numerical Value Type
  1. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  2. "Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the v...

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

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  5. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

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  6. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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  7. Let f: R->R be a differentiable function with f(0)=1 and satisfy...

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

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

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  10. If x^(3)+3x^(2)-9x+lamda is of the form (x-alpha)^(2)(x-beta) then lam...

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

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

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

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

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

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

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