Differentiate the following functions?

[LilTaru]

Homework Statement

Differentiate the following functions:

a) x³cos(5x)sin(cubedroot(x) + 2)

b) tan(1 + cos²(xsin³(x² + 1)))

c) (x² + (x² + (x² + 1)^-1)^-1)^-1

Homework Equations

The Attempt at a Solution

These are the most terrifying questions I have seen thus far in my textbook... I have no idea what differentiation rules to use or how to even begin to tackle these questions?

 

[micromass]

a) apply the product rule 2 times. You'll also need to apply the chain rule to find the separate derivatives...

 

[LilTaru]

Apply the product rule between x³ and cos(5x) and then again between cos(5x) and sin(cubedroot(x) + 2)?

 

[micromass]

Apply the product rule between x³ and cos(5x)sin(cubedroot(x) + 2). Then a second time between cos(5x) and sin(cubedroot(x) + 2). You'llalso need to apply the chain rule for cos(5x) and sin(cubedroot(x) + 2)...

 

[LilTaru]

Okay I tried this strategy:

b) Let u = x² + 1
Let t = sin u
Let s = t³
Let r = xs
Let q = cos r
Let p = q²
Let o = 1 + p
Let y = tan o

Then dy/dx = dy/do * do/dp * dp/dq * dq/dr * dr/ds * ds/dt * dt/du * du/dx

c) Let u = (x² + 1)^-1
Let t = (x² + u)^-1
Let s = (x² + t)^-1
Let y = s

Then dy/dx = dy/ds * ds/dt * dt/du * du/dx

Is this on the right track?