Differentiate with respect to x:tan 3x

1.	Differentiate with respect to x:tan 3x
Answer» Chain rule: If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx Let y = tan 3x If t = 3x then tan 3x = tan t or y = tan t dy/dt = sec² t dt/dx = 3 Now, dy/dx = dy/dt x dt/dx = 3 sec² t Substituting the value of t back, we get dy/dx = 3sec² 3x

Answer»

Chain rule:

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

Let y = tan 3x

If t = 3x then tan 3x = tan t or y = tan t

dy/dt = sec² t

dt/dx = 3

Now,

dy/dx = dy/dt x dt/dx = 3 sec² t

Substituting the value of t back, we get

dy/dx = 3sec² 3x

Discussion

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