Differentiate with respect to x.cos x3

1.	Differentiate with respect to x.cos x3
Answer» Chain rule: If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx Let y = cos x³ If t = x³ then cos x³= cos t or y = cos t dy/dt = -sin t dt/dx = 3x² Now, dy/dx = dy/dt x dt/dx = 3 x² (-sin t) Substituting the value of t back, we get dy/dx = 3 x² (-sin x³) = -3 x² sin x³

Answer»

Chain rule:

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

Let y = cos x³

If t = x³ then cos x³= cos t or y = cos t

dy/dt = -sin t

dt/dx = 3x²

Now,

dy/dx = dy/dt x dt/dx = 3 x² (-sin t)

Substituting the value of t back, we get

dy/dx = 3 x² (-sin x³)

= -3 x² sin x³

Discussion

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