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what is the derivative of 1/x^5-9 with respect to x^2
Asked by gamingwired318 | 16 Jun, 2022, 20:37: PM
Let f(x) = ![begin mathsize 14px style fraction numerator 1 over denominator x to the power of 5 minus 9 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/31d1334c05c6e5c9864f6335ebb6df44.png)
![begin mathsize 14px style fraction numerator 1 over denominator x to the power of 5 minus 9 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/31d1334c05c6e5c9864f6335ebb6df44.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/7a0e4714d55e3a55488a44369a61cae0.png)
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](https://images.topperlearning.com/topper/tinymce/cache/48ceb1a22d707b452f2be55dd1be480d.png)
Answered by Thiyagarajan K | 16 Jun, 2022, 21:47: PM
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