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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
- If x^p.y^q=(x+y)^(p+q) , show that dy/dx=y/x ;
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- If y = x^y, prove that (dy)/(dx) = (y^2)/(x(1 - y log x))
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- Differentiate the following w.r.t.x. If y^x = e^(y - x), prove that ...
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- If x^x + y^x = 1, prove that : dy/dx = -[(x^x (1+logx) + y^x.logy)/(x....
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- If x^y + y^x=1, find dy/dx
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- If x^y + y^x = log a, find dy/dx.
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- Show that if x^y + y^x = m^n, then: dy/dx = - (y^x logy +yx^(y-1))/...
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- Find the derivative of the function given by f(x) = (1+x)(1+x^2)(1+x^4...
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- Differentiate (x^2-5x+8)(x^3+7x+9) by using product rule.
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- Differentiate(x^2-5x+8)(x^3+7x+9) by expanding the product to obtain a...
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- Differentiate (x^2-5x+8)(x^3+7x+9) by logarithmic differentiation.
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- If y = (sqrtx)^(sqrtx^(sqrtx))......... to infty), prove that dy/dx = ...
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- If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))), show that (2y - 1) (dy)/...
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- If y = sqrt(3^x+sqrt(3^x+sqrt(3^x+….......oo))), then prove that : (2y...
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- If y = x^y, prove that (dy)/(dx) = (y^2)/(x(1 - y log x))
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- If y = (cosx)^(cosx^(cosx……..to infty)) prove that dy/dx = (-y^2 tanx)...
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- If y=(tanx)^((tanx)^((tanx)^...oo)), then prove that (dy)/(dx)=2 at x=...
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- If y = (x^(x^(x)….......to oo)), prove that xdy/dx=y^2/(1-ylogx).
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- Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : 1+2x
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- Find (a) (dy)/(dx) and (b) = (d^2y)/(dx^2) when y is given by : ax^3...
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