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Differentiate the following : y = co...

Differentiate the following :
`y = cos (a^(3) + x^(3) )`

Text Solution

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The correct Answer is:
`-3 x^(2) sin (a^(3) + x^(3) )`
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FULL MARKS-DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 3 (Differentiate the following)
  1. Differentiate the following : h(t) = (t - (1)/(t) )^(3//2)

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  2. Differentiate the following : f(t) = root(3) (1 + tan t)

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  3. Differentiate the following : y = cos (a^(3) + x^(3) )

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  4. Differentiate the following : y =e^(-mx)

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  5. Differentiate the following : y = 4 sec 5x

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  6. Differentiate the following : y = (2x-5)^(4) (8x^(2) - 5)^(-3)

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  7. Differentiate the following : y= (x^(2) + 1) root(3) ( x^(2) + 2)

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  8. Differentiate the following : y = xe^(-x^2)

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  9. Differentiate the following : s(t) = root(4)((t^3 + 1)/(t^(3) -1))

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  10. Differentiate the following : f(x) = (x)/(sqrt(7-3x))

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  11. Differentiate the following : y = tan ( cos x)

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  12. Differentiate the following : y = (sin^(2) x)/(cos x)

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  13. Differentiate the following : y= 5^(-(1)/(x))

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  14. Differentiate the following : y = sqrt(1+2 tan x)

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  15. If y = sin^(3) x + cos^(3) x then find dy/dx.

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  16. Differentiate the following : y = sin^(2) ( cos kx)

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  17. Differentiate the following : y = (1+ cos^(2) x)^(6)

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  18. Differentiate the following : y= (e^(3x))/(1 + e^(x))

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  19. Differentiate the following with respect to x: y = sqrt( x sqrt(x))

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  20. Differentiate the following with respect to x: y =e^(x cos x)

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