Question

Find the derivative of the function.
y = sin(tan 8x)

Answer 1

Use the product rule. First times the derivative of the second plus the second times the derivative of the first.

Answer 2

Oh no I see.

Answer 3

Sorry this is sin of tan8x right?

Answer 4

sin times tan 8x

Answer 5

Wait, is it sin of tan8x or sinx times tan8x? There is a big difference there.

Answer 6

sinx times tan 8x

Answer 7

ok product rule it is then. Your first term is the sinx and your second term is tan(8x)

Answer 8

The derivative of sinx is cosx

Answer 9

how do u then do tan (8x)

Answer 10

i know how to do the first part.

Answer 11

and the derivative of tan8x is \[\frac{ d }{ dx } \tan(8x)= 8\sec ^{2}(8x) \]

Answer 12

how do u let to that

Answer 13

well the derivative of tan(x) is equal to sec^2(x) so tan8x is equal to sec^28x then you just multiply the function by the derivative of 8x, which is 8.