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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, 08:36: PM

Expert Answer

Let f(x) =

begin mathsize 14px style square root of sin space x space plus space 3 x squared end root space end style

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

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

Answered by Thiyagarajan K | 16 Jun, 2022, 08:49: PM