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Differentiate sin (x²+1) w.r.t. x

Solution: We have,

Let y = sin (x² + 1). Putting u=x² + 1, we get

y = sin u and u=x² + 1 

∴ dy/du= cos u and du/dx = 2x

Now, dy/dx = dy/du × du/dx

dy/dx = (cos u).2x = 2x cos (x² + 1)    [∵u=x²+1]

Hence, d/dx{sin (x² + 1)} = 2x cos (x²+1)