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If u, v and w are functions of x, then s...

If u, v and w are functions of x, then show that`d/(dx)(udotvdotw)=(d u)/(dx)vdotw+udot(d v)/(dx)dotw+udotv(d w)/(dx)`in two ways - first by repeated application of product rule, second by logarithmic differentiation.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.5
  1. Differentiate the functions given in w.r.t. x : cos2x+sin3x.

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  2. Differentiate the functions given w.r.t. x: sqrt(((x-1)(x-2)/((x-3)(x-...

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  3. Differentiate the functions given in w.r.t. x : (logx)^(cosx)

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  4. Differentiate the functions given in w.r.t. x : x^(x)-2^(sinx)

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  5. Differentiate the functions given in w.r.t. x : (x+7)^(2)*(x+4)^(3).

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  6. Differentiate the functions given w.r.t. x:(x+1/x)^x+x^((1+1/x))

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  7. Differentiate the functions given in w.r.t. x : (logx)^(x)+x^(logx)

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  8. Differentiate the functions given in w.r.t. x : (sinx)^(x)+sin^(-1)s...

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  9. Differentiate the functions given in w.r.t. x : x^(sinx)+(sinx)^(cos...

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  10. Differentiate the functions given in w.r.t. x : x^(xcosx)+(x^(2)+1)/...

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  11. Differentiate the functions given in w.r.t. x : (xcosx)^(x)+(xsinx)^...

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  12. Find dy/dx of the function given in : x^(y)+y^(x)=b

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  13. Find dy/dx of the function given in : y^(x)=x^(y)

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  14. Find (dy)/(dx), when: (cosx)^(y)=(cosy)^(x)

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  15. Find (dy)/(dx)of the functions givenx y=e^((x-y))

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  16. Find the derivative of the function given by f(x)=(1+x)(1+x^2)(1+x^4)(...

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  17. Differentiate (x^2-5x+8)(x^3+7x+9) in three ways mentioned below:(i) ...

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  18. If u, v and w are functions of x, then show thatd/(dx)(udotvdotw)=(d u...

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