Question

Differentiate function
f(x)= [(1/2)x]^5

the outside power, is messing me up

Answer 1

\[(\frac{1}{2}x)^5\]

Answer 2

if that's true

\[\frac{1}{32}*5x^4\]

Answer 3

so 5x^4/32?

Answer 4

yes

Answer 5

thanks you soo much

Answer 6

To see what is really going on under the hood you can apply the chain rule here, and make a substitution by setting u=(1/2)x\[\rightarrow\]du/dx=1/2


The equation can then be rewritten as:
\[y=u^{5}\]\[\rightarrow\]
dy/du=\[5u ^{4}\]
From the chain rule dy/dx=dy/du * du/dx = (\[5u ^{4} * 1/2\]

Since u = (1/2)x then dy/dx =\[ 5 (1/16)x ^{4} * 1/2\]
= \[(5/32)x ^{4}\]