Differentiate with respect to x:sin2 (2x + 3)

1.	Differentiate with respect to x:sin2 (2x + 3)
Answer» Chain rule: If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx d/dx sin² (2x + 3) = 2 sin (2x + 3) * d/dx {sin(2x + 3)} = 2 sin (2x + 3) * cos(2x + 3) * d/dx (2x + 3) = 2 sin (2x + 3) * cos (2x + 3) * 2 = 4 sin (2x + 3) cos (2x + 3) = 2 sin (4x + 6) [Using identity: 2sin x cos x = sin 2x]

Answer»

Chain rule:

If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx

d/dx sin² (2x + 3) = 2 sin (2x + 3) * d/dx {sin(2x + 3)}

= 2 sin (2x + 3) * cos(2x + 3) * d/dx (2x + 3)

= 2 sin (2x + 3) * cos (2x + 3) * 2

= 4 sin (2x + 3) cos (2x + 3)

= 2 sin (4x + 6)

[Using identity: 2sin x cos x = sin 2x]

Discussion

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