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Prove that the derivative of (a) an odd ...

Prove that the derivative of (a) an odd function is an even function;

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Prove that the derivative of an even function is an odd function and that of an odd function is an even function.

Prove that the product of two odd functions is an even function while their sum is an odd function.

The derivative of an even function is always an odd function.

Derivative of odd function is

Prove that the product of two even or two odd functions is an even function, whereas the product of an even and an odd function is an odd function.

Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

Statement -1 : Integral of an even function is not always on odd function. Statement-2: Integral of an odd function is an even function.

A DAS GUPTA-Differentiation-Exercise
  1. Let f((x+y)/(2))=1/2 |f(x) +f(y)|for all real x and y, if f '(0) exist...

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  2. A function f(x) is so defined that for all real x,{f(x)}^n = f(nx). Pr...

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  3. Prove that the derivative of (a) an odd function is an even function;

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  4. Prove that the derivative of a periodic function of period T is a peri...

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  5. Let f(x) be a function satisfying the condition f(-x) = f(x) for all r...

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  6. A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)...

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  7. Find the sum of series sum(r=1)^nr.x^(r-1), using calculus.

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  8. Differential coefficient of log2(log2x)w.r.t x is

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  9. If f(x)=logx(logex) then f'(e)=

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  10. If x=a (cos t +log (tan ((t)/(2)) )) ,y =a sin t ,then (dy)/(dx) =

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  11. Let f'(x) = sin(x^2) and y = f(x^2 +1) then dy/dx at x=1 is

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  12. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  13. If f'(x)=sin x^2 and y=f(x^2+1) then dy/dx=

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  14. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  15. If tany = (2t)/(1-t^2) and sin x = (2t)/(1+t^2) then (dy)/(dx)=

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  16. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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  17. If x^2y +y^3=2, the value of (dy)/(dx) at the point (1,1) is

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  18. Let f(x)={(tan)pi/4+tanx}{(tan)pi/4+(tan)(pi/4-x)}and g(x)=x^2+1. Then...

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  19. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

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  20. IF y = 1 / (1+ x + x^2 + x^3), then value of (d^2y) / dx^2 at x = 0 is

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