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

If `y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * *infty` show that `(dy)/(dx) = y `

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If y = x- (x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+* * * prove that (1 + x) (dy)/(dx) = 1

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If y = (x - 2 )/ (x + 2) , show that 2x * (dy)/(dx) = 1 - y^(2) .

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(x + 2y^(3)) dy/dx = y

CHHAYA PUBLICATION-DIFFERENTIATION-Short AnswerType Questions
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  6. Find the derivatives of the following functions : (1 + sin 2 x - co...

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  8. Find the derivatives of the following functions : (1 + x + x^(2))/...

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  9. In each of the following cases show that (dy)/(dx) = 0 , when ...

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  10. In each of the following cases show that (dy).(dx)=0, when y = (...

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  11. If y = (x)/(x + 4) prove that x(dy)/(dx)+y (y-1) = 0

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  12. If y = cosec theta + cot theta , prove that 2(dy)/(d theta)+ y^(2)...

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

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  14. If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * *infty sho...

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  15. If y = x- (x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+* * * prove that (1 ...

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  16. If y = (f(x))/(g(x)) , where f (x) and g (x) are two differentiable f...

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  17. If y = sqrt(x/(a))-sqrt(a/(x)) show that 2xy (dy)/(dx)=(x)/(a)-(a)/(x...

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  18. If f (x) is an even function and f'(0) exists, show that f'(0) = 0 ...

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  19. y={:((x^(2)-4x + 3 )/(x^(2)+2x-3)," ""when"xne1):} {:(=-(1)/(...

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  20. If {:(f(x)=1+x," ""when"x ne 1),(=1," ""when"0lexle1),(2x^(2)+4x+5, " ...

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