Find dy/dx , if y = e^x^2+2 + sin (5x^2+2) + 3 cos^2x?

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Answer 1 · 2018-07-28T14:04:03

$dy/dx=2xe^{x^2+2}+10x\cos(5x^2+2)-3\sin2x$

Given function:

$y=e^{x^2+2}+\sin(5x^2+2)+3\cos^2x$

differentiating above equation w.r.t. $x$ using chain rule as follows

$dy/dx=d/dx(e^{x^2+2})+d/dx\sin(5x^2+2)+3d/dx\cos^2x$

$=e^{x^2+2}d/dx(x^2+2)+\cos(5x^2+2)d/dx(5x^2+2)+3(2\cos x)d/dx(\cosx)$

$=e^{x^2+2}(2x)+\cos(5x^2+2)(10x)+3(2\cos x)(-\sinx)$

$=2xe^{x^2+2}+10x\cos(5x^2+2)-3\sin2x$