Question

y=sin [lnx + e^x + x^2/2] find dy / dx​

Answer 1

Answer:

dy/dx = cos[1/x + e^x + x^2/2]*(1/x + e^x + x^2/2)

Explanation:

Given, y = sin[lnx + e^x + x^2/2]

take u = (lnx + e^x + x^2/2)

then y = sin[u]

differentiating on both sides

we get, (dy/dx) = cos[u]*d(u)/dx

where du/dx = 1/x + e^x + x^2/2

therefore dy/dx = cos[1/x + e^x + x^2/2]*(1/x + e^x + x^2/2)