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| Summary |
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 A function f(x) is said to be derivable at a point x = a if |
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 Left hand derivative Lf '(a) |
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 Right hand derivative Rf '(a) |
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 f'(a) exists at x = a iff Lf' (a) = Rf'(a) |
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 Derivability implies continuity |
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Derivative of a constant function is zero. |
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Logarithmic Differentiation |
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is obtained by taking log on both sides and then differentiating both sides. |
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Differentiation of functions expressed in parametric form. If x = x(t)
and y = y(t) then  |
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| Step 1: |
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| Step 2: |
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| Differentiate the terms containing x, y or both xy with respect to x. |
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While differentiating the terms containing y or power of y, first
differentiate with respect to y, then multiply by  . |
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| Step 3: |
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| Step 4: |
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If y
= f(x) is differentiable then  is called the first order derivative
of y = f(x) if is further
differentiable the  is called the second order derivative of f(x). |
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| Derivatives of standard functions |
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