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

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

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A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all x , y in R and f(x)!=0 for all x in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
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  2. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

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  3. If f(x)=x|x|, then prove that f^(prime)(x)=2|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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  8. Let y=1n(1+cosx)^2. Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal

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

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

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

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

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

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  17. If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...

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  18. If d/(dx)[(x^m-A1x^(m-1)+A2x^(m-2)-.......+(-1)^m Am)e^x]=x^m e^x , f...

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