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Let u = tan 5x such that you are differentiating 4u3 with respect to x.

Differentiating the above becomes

12u2 times du/dx

Now we obtain du/dx i.e. differentiate tan 5x with respect to x. We let w = 5x such that you are differentiating tan w with respect to x.

Differentiating tan w gives sec2 w times dw/dx.

dw/dx = 5.

Combine the results, and you get

12u2 times sec2 w times 5

= 12 tan2 5x sec2 5x times 5

= 60 tan2 5x sec2 5x

Differentiating the above becomes

12u2 times du/dx

Now we obtain du/dx i.e. differentiate tan 5x with respect to x. We let w = 5x such that you are differentiating tan w with respect to x.

Differentiating tan w gives sec2 w times dw/dx.

dw/dx = 5.

Combine the results, and you get

12u2 times sec2 w times 5

= 12 tan2 5x sec2 5x times 5

= 60 tan2 5x sec2 5x

Date Posted:
1 month ago