Eric Nicholas K's answer to mint's Secondary 4 A Maths Singapore question.
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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:
5 years ago