How do you find the derivative of y=sinxtan^3(x)?

Answer 1

use the product rule

y = sinx tan^3(x)
y' = cosx tan^3(x) + sinx (tan^3(x))'
for tan^3(x), use the chain rule and you get

y' = cosx tan^3(x) + sinx(3tan^2(x) sec^2(x))

Now we can massage things a bit:

sin^3/cos^2 + 3sin^3/cos^4
sin^3*cos/cos^3 + 3sin^3/cos^4
tan^3(cos + 3sec)

lots of ways