Recall that (cot x) = −csc^2 x. Here we use the Chain Rule to find the derivative: =
(−csc^24 x)(4) = −4csc^2 (4x).
- 6cos 3x cos 4x − 8 sin 3x sin 4x
Recall that (sin x) = cos x and that (cos x) = −sin x. Here we use the Product Rule to find
the derivative: = 2[(sin 3x)(4) + (cos 4x)(cos 3x)(3)]. This can be simplified to = 6cos
3 x cos 4x − 8sin 3x sin 4x.
- (secθ)(sec^2 (2θ))(2) + (tan2θ)(secθ tanθ)
Recall that (tan x) = sec^2 x and that (sec x) = sec x tan x. Using the Product Rule and the
Chain Rule, we get = (secθ)(sec^2 (2θ))(2) + (tan^2 θ)(secθ tanθ).
- cos
Recall that (sin x) = cos x and that (cos x) = −sin x. Using the Chain Rule, we get =
.
29.
We take the derivative of each term with respect to x: =
.
Next, because = 1, we can eliminate that term to get =
.
Next, group the terms containing on one side of the equals sign and the other terms on the
other side: = sin x + cos x.
