Question

if y =cos (t)^3 +lnt ,dy/dx =??
answer this
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Answer 1

I assume you have to find dy/dt because y is a function of t here.

See the attachment for desired solution.

What you witnessed just now is called chain rule. First differentiate cost³ with respect to t³ and then differentiate t³ with respect to t

If you still don't understand, assume t³ = z

Then it becomes cosz

so differentiate cosz with respect to z, and then differentiate z = t³ with respect to t.