What is the second derivative for $y(x)=5e^(pi x)+cos (y(x))$ ?

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Answer 1 · 2015-09-26T00:44:00

$y''=(5pi^2e^(pix) ((1+siny)^2-5e^(pix)cosy))/(1+siny)^3$

$d/dx(y(x))=d/dx(5e^(pix)+cos(y(x))$

$y'=5pie^(pix)-siny*y'$

$y'=(5pie^(pix))/(1+siny)$

$d/dx(y')=(5pi^2e^(pix)*(1+siny)-5pie^(pix)*cosy*y')/(1+siny)^2$

$y''=(5pi^2e^(pix)*(1+siny)-5pie^(pix)*cosy (5pie^(pix))/(1+siny))/(1+siny)^2$

$y''=(5pi^2e^(pix)*(1+siny)^2-25pi^2e^(2pix)*cosy)/(1+siny)^3$

$y''=(5pi^2e^(pix) ((1+siny)^2-5e^(pix)cosy))/(1+siny)^3$

What is the second derivative for y(x)=5e^(pi x)+cos (y(x))y(x)=5e^(pi x)+cos (y(x)) ?