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Differentiate the following functions : ...

Differentiate the following functions :
`tan ^-1(Ln (x^3+2x+5))`

Text Solution

Verified by Experts

Let y = `tan^-1(In(x^3+2x+5))`
`implies dy/dx=-1/(1+(In(x^3+2x+5))^2)(3x^2+2)/((x^3+2x+5)`
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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
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  2. Find the derivative of the following functions w.r.t.x: y=e^(4x)/x^2

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  3. Differentiate the following functions : tan ^-1(Ln (x^3+2x+5))

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  4. Differentiate the following functions : "cosec"^-1(e^(2cosx))

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  5. Differentiate the following functions : (cos^-1(1-3x))^2

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  6. Find dy/dx, when x=acos t + at, y = asin t -at, where t is the param...

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  7. Find dy/dx, when x log x + y log y + xy - 5x + 2y + 3 = 0

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  8. Find dy/dx, when y = x^x+(sin x )^(cosx)

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  9. If the radius of a circle changes at a uniform rate of 2 cm/s, find th...

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  11. Find the equation of the tangent and the normal at the point (0, -1) t...

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  13. For the function f(x) = 2x^3-8x^2+10x+5, find the interval (s) in wh...

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  14. Investigate the increasing or decreasing behaviour of the following fu...

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  15. If xgt0,ygt0 and x+y=1, then find the minimum value of x log x + y log...

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  16. Evaluate the following integrals : intx.e^xdx

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  17. Evaluate the following integrals : inte^(tan^-1x)/(1+x^2)dx

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  18. Evaluate the following integrals : intsecx(secx+tanx)dx

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  19. Evaluate the following integrals : int3^6abs(x-4)dx

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  20. Solve the following differential equations : xdy+ydx=0,at x=1,y=1

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