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what is the derivative of under root sinx+3x^2 with respect to x^2
Asked by gamingwired318 | 16 Jun, 2022, 20:36: PM
Let f(x) = ![begin mathsize 14px style square root of sin space x space plus space 3 x squared end root space end style](https://images.topperlearning.com/topper/tinymce/cache/87dc55a0764368870cdb36d9596b9d4c.png)
![begin mathsize 14px style square root of sin space x space plus space 3 x squared end root space end style](https://images.topperlearning.com/topper/tinymce/cache/87dc55a0764368870cdb36d9596b9d4c.png)
![begin mathsize 14px style fraction numerator d f over denominator d x end fraction space equals space fraction numerator 1 over denominator 2 square root of sin space x space plus space 3 space x squared end root end fraction cross times open parentheses cos space x plus space 6 x space close parentheses space equals space fraction numerator open parentheses cos space x plus space 6 x space close parentheses over denominator 2 square root of sin space x space plus space 3 space x squared end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/f8b90a9ad663cd64841cf1abb65f5a62.png)
Let g(x) = x2
dg/dx = 2 x
![begin mathsize 14px style fraction numerator d f over denominator d g end fraction space equals space fraction numerator d f divided by d x over denominator d g divided by d x end fraction space equals space fraction numerator stretchy left parenthesis space cos space x space plus space 6 space x stretchy right parenthesis over denominator 2 space square root of sin space x space plus space 3 space x squared end root space cross times space 2 x end fraction space equals space fraction numerator stretchy left parenthesis space cos space x space plus space 6 space x stretchy right parenthesis over denominator 4 x square root of sin space x space plus space 3 space x squared end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/b8d4271c8706dbb3fcdf82cd3c3024b3.png)
Answered by Thiyagarajan K | 16 Jun, 2022, 20:49: PM
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Asked by gamingwired318 | 16 Jun, 2022, 20:36: PM