Differentiate with respect to x:sin 4x

1.	Differentiate with respect to x:sin 4x
Answer» Chain rule: If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx Let y = sin 4x If 4x = t then sin4x = sin t or y = sin t dy/dt = cos t dt/dx = 4 Now, dy/dx = dy/dt x dt/dx = 4 cos t Substituting the value of t back, we get dy/dx = 4 cos 4x

Answer»

Chain rule:

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

Let y = sin 4x

If 4x = t then sin4x = sin t or y = sin t

dy/dt = cos t

dt/dx = 4

Now,

dy/dx = dy/dt x dt/dx = 4 cos t

Substituting the value of t back, we get

dy/dx = 4 cos 4x

Discussion

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