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Working  Rules

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IV Working  Rules : –

 If  f   and   g   are  differentiable  on  ( a , b )  and ∀ x ∈ ( a , b ) ,   then

     1.   \frac{d}{dx}[  f ( x )  ±  g ( x ) ]   =     \frac{d}{dx}  f ( x )     ±     \frac{d}{dx} g ( x )

2.    \frac{d}{dx}k   f ( x )     =    k \frac{d}{dx}   f ( x )

3.    \frac{d}{dx}[  f ( x )  ·  g ( x ) ]   =    f ( x )  · \frac{d}{dx} g ( x )      +      g ( x )  · \frac{d}{dx} f ( x )

4.  \frac{d}{dx} \left (\frac{f(x)}{g(x)} \right )  =  \frac{g(x) \times \frac{d}{dx} \ f(x) \ - \ f(x) \ \times \frac{d}{dx} \ g(x)}{\left [ g\left ( x \right ) \right ]^{2}}

5. \frac{d}{dx} \left (\frac{1}{g(x)} \right )  =  - \frac{\frac{d}{dx} \ g(x)}{\left [ g\left ( x \right ) \right ]^{2}}   or   \frac{d}{dx} \left (\frac{1}{g(x)} \right )  = - \frac{\ g(x)}{\left [ g\left ( x \right ) \right ]^{2}}

V y_2 = y^{\prime^\prime}   =    \frac{d^2y}{dx^2}    =    (y)

 VI Chain   Rule   : –

\frac{dy}{dx} = \frac{dy}{dz} \times \frac{dz}{dx}

 

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