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If the function f(x)=x^(3)+e^(x//2)andg...

If the function `f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x)`, then the value of `g'(1)` is

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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. If y is a function of x then (d^2y)/(dx^2)+y \ dy/dx=0. If x is a func...

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  2. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive functi...

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  3. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

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

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  5. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(1)/(4) is equal to

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  6. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

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  7. If y=(sin^(-1)(sinalphasinx)/(1-cosalphasinx)), then y'(0) is equal to

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  8. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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  9. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

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  10. If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...

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  11. If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )(...

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  12. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

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  13. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

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  14. Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...

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  15. if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...

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  16. If f(x)=-(x^(3))/(3)+x^(2)sina.sin2a-5sin^(-1)(a^(2)-8a+17),then

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  17. Let f and g be differentiable functions satisfying g(a) = b,g' (a) = ...

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  18. The derivative of the function, f(x)=cos^(-1){(1)/(sqrt13)(2cosx-3sin...

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  19. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

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  20. Let y=ln(1+cosx)^(2), then the value of(d^(2)y)/(dx^(2))+(2)/(e^(y//2)...

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