Limits and Derivatives

Limits and Derivatives

Question

Find the derivatives of the following functions :

space space space fraction numerator 1 over denominator square root of straight x end fraction

Answer

Let        space space space space space space space space straight y space equals space fraction numerator 1 over denominator square root of straight x end fraction equals straight x to the power of negative 1 half end exponent

∴       space space space space space space space space space dy over dx equals straight d over dx left parenthesis straight x to the power of negative 1 half end exponent right parenthesis space equals space minus 1 half straight x to the power of negative 1 half minus 1 end exponent         space space space space space space open square brackets because straight d over dx left parenthesis straight x to the power of straight n right parenthesis equals space nx to the power of straight n minus 1 end exponent close square brackets

       

                space space space space space space space equals space space minus 1 half straight x to the power of negative 3 over 2 end exponent

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