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If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... ...

If `y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+...` , then `(dy)/(dx)=` a. `y+1` b. `y-1` c. `y` d. `y^2`

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Given,`y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+...`
`(dy/dx)=(d/dx)(1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+...)`
`(dy/dx)=(d/dx)1+(d/dx)x/(1!)+(d/dx)(x^2)/(2!)+(d/dx)(x^3)/(3!)+...`
`(dy/dx)=(0+1+(2x^2)/(2!)+(3x^2)/(3!)+...)`
So(dy/dx)=y
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RD SHARMA-DERIVATIVES-Solved Examples And Exercises
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  2. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

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  3. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

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  7. Write the derivative of f(x)=3 \ |2+x| at x=-3.

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  9. Let f(x)=x-[x], x in RR, then f^(prime)(1/2) is a. 3/2 b. 1 c. 0 d. -1

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  10. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

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  11. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

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  13. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

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  14. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

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