# Thread: chain rule derivs.

1. ## chain rule derivs.

f() = ln(sin(8))

h(w) = w^3 ln(14w)

can someone show me how to do these...much thanks...

mathaction

2. Originally Posted by mathaction
f() = ln(sin(8))

h(w) = w^3 ln(14w)

can someone show me how to do these...much thanks...

mathaction
hi,

use chain rule:

$f'(\alpha)=\frac1{\sin(8 \alpha)} \cdot \cos(8 \alpha) \cdot 8 = \frac{8 \cdot \cos(8 \alpha)}{\sin(8 \alpha)} = \frac8{\tan(8\alpha)}$

use product rule and chain rule:

$h'(w)=\ln(14w) \cdot 3 \cdot w^2 + w^3 \cdot \frac1{14w} \cdot 14 = w^2\left(3 \cdot \ln(14w) + 1 \right)$