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what is the derivative of 1/x^5-9 with respect to x^2
Asked by gamingwired318 | 16 Jun, 2022, 08:37: PM
Expert Answer
Let f(x) = begin mathsize 14px style fraction numerator 1 over denominator x to the power of 5 minus 9 end fraction end style
begin mathsize 14px style fraction numerator d f over denominator d x end fraction equals fraction numerator negative 4 x to the power of 4 over denominator open parentheses x to the power of 5 minus 9 close parentheses squared end fraction end style
Let g(x) = x2
 
dg/dx = 2x
 
begin mathsize 14px style fraction numerator d f over denominator d g end fraction equals fraction numerator d f divided by d x over denominator d g divided by d x end fraction space equals space fraction numerator negative 4 x to the power of 4 over denominator 2 x open parentheses x to the power of 5 minus 9 close parentheses squared end fraction space equals space fraction numerator negative 2 space x cubed over denominator open parentheses x to the power of 5 minus 9 close parentheses squared end fraction end style
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