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Solve the following: f(x) = -x for -2le ...

Solve the following: `f(x) = -x` for -2`le` x `<` 0,
= 2x for 0`le` x`le` 2,
=`frac{18-x}{4}` for 2`<`x`le` 7,
g(x) = 6-3x, 0`le` x`<` 2,
=`frac{2x-4}{3}` , 2`le` x `<` 7.
Let u(x)= f[g(x)], v(x)=g[f(x)] and w(x)=g[g(x)]
Find each derivative at x=1, if it exists,
i.e., find the u'(1), v'(1) and w'(1). If it doesn't exist, then explain why?

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CHETANA PUBLICATION-Differentiation-Exercise
  1. Solve the following: f(x) = -x for -2le x < 0, = 2x for 0le xle 2, ...

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  2. Differentiate the following w.r.t. x : sin(x^2 + x)

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  3. Differentiate the following w.r.t. x : cos(log x)

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  4. Differentiate the following w.r.t. x : cot (x^3)

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  5. Differentiate the following w.r.t. x : log(log x)

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  6. Differentiate the following w.r.t. x : 9^(\log(3) (sin x)) + 25^(log(5...

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  7. Differentiate the following w.r.t x: cos^(-1) (2^x)

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  8. Differentiate the following w.r.t. x: cot^(-1) (frac{1}{x})

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  9. Differentiate the following w.r.t. x: sin^(-1) (2 cos^2 x -1)

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  10. Differentiate the following w.r.t. x: cosec^(-1) frac{1}{3x- 4 x^3}

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  11. Differentiate the following w.r.t. x: sin^(-1) (frac{a sin x + b cos ...

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  12. Differentiate the following w.r.t. x: tan^(-1) (frac{6x}{1+ 16 x^2})

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  13. Differentiate the following w.r.t. x: e^(3x) sin^2 x log x

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  14. Differentiate the following w.r.t. x: (x+1)^(3/2) (2x+3)^(5/2) (3x+4)^...

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  15. Differentiate the following w.r.t. x: x^x + a^a

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  16. Differentiate the following w.r.t. x: (sin x)^(tan x)

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  17. Find dy/dx if, x^2 + e^(xy) = y^2 + log(x+y)

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  18. Find dy/dx if, e^(2x) + e^(2y) = e^(2(x+y))

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  19. If y=1+ xe^y , then show that dy/dx =frac{e^y}{2-y}

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  20. If y=log((1-x^2)/(1+x^2)), then (dy)/(dx) is equal to

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  21. If sqrt (1-x^2) + sqrt (1-y^2) = a(x-y), then show that dy/dx = sqrt...

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