Differentiate with respect to x:cos 5x

1.	Differentiate with respect to x:cos 5x
Answer» Chain rule: If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx Let y = cos 5x If t = 5x then cos 5x = cos t or y = cos t dy/dt = -sin t dt/dx = 5 Now, dy/dx = dy/dt x dt/dx = -5 sin t Substituting the value of t back, we get dy/dx = -5 sin 5x

Answer»

Chain rule:

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

Let y = cos 5x

If t = 5x then cos 5x = cos t or y = cos t

dy/dt = -sin t

dt/dx = 5

Now,

dy/dx = dy/dt x dt/dx = -5 sin t

Substituting the value of t back, we get

dy/dx = -5 sin 5x

Discussion

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