Limits and Derivatives

Find the derivative of the following : x -4 (3 - 4x -5 ) - Wired Faculty

Question

Find the derivative of the following :

x^-4 (3 - 4x^-5)

Solution

Let y = x^-4 (3 - 4x^-5)
$rightwards double arrow$ y = 3 x^-4-4x^-9
Differentiating both sides w.r.t. x, we get
$space space space space space space space space space space space space space space space space space space space dy over dx equals straight d over dx open parentheses 3 straight x to the power of negative 4 space end exponent minus 4 straight x to the power of negative 9 end exponent close parentheses equals straight d over dx open parentheses 3 straight x to the power of negative 4 end exponent close parentheses minus straight d over dx left parenthesis 4 straight x to the power of negative 9 end exponent right parenthesis$
$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 straight d over dx left parenthesis straight x to the power of negative 4 end exponent right parenthesis minus 4 straight d over dx left parenthesis straight x to the power of negative 9 end exponent right parenthesis equals 3 left parenthesis negative 4 right parenthesis straight x to the power of negative 5 end exponent minus 4 left parenthesis negative 9 right parenthesis straight x to the power of negative 10 end exponent$
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