What is the derivative of $e^{sin (x^{2})}$ $e^sin(x^2)$ ?

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Answer 1 · 2016-11-18T12:03:16

$2 x e^{sin (x^{2})} cos (x^{2})$ $2xe^(sin(x^2))cos(x^2)$

$f (x) = e^{sin (x^{2})}$ $f(x) = e^(sin(x^2))$

$f (x) = e^{g (x)}$ $f(x) = e^(g(x))$ Where $g (x) = sin (x^{2})$ $g(x)= sin(x^2)$

$f'(x) = d/dx e^(g(x)) = e^(g(x))* g'(x)$ By the Chain Rule

$f'(x) = e^(sin(x^2)) * cos (x^2) * d/dx x^2$ By the Chain Rule again

$f'(x) = e^(sin(x^2)) * cos (x^2) * 2x$

$f'(x) = 2xe^(sin(x^2))cos(x^2)$

What is the derivative of e^sin(x^2)esin(x2)e^sin(x^2)?