If #h(x)=p(x) * q(x) * r(x)# what is #h'#?

1 Answer
Alan P.
Mar 2, 2015

Assuming the question is:
If #h(x) = p(x)*q(x)*r(x)#
write an expression for #h'(x)#

Answer:
#h'(x) = p'(x)*q(x)*r(x) + p(x)*q'(x)*r(x) + p(x)*q(x)*r'(x)#

Reasoning:
Let #s(x) = q(x)*r(x)#
Then # h(x) = p(x)*s(x)#
and #h'(x) = p'(x)*s(x) + p(x)*s'(x)# by derivative product rule

#s'(x) = q'(x)*r(x) + q(x)*r'(x)#

Substituting this back into our formula for #h'(x)#
we get
#h'(x) = p'(x)*q(x)*r(x) + p(x)*q'(x)*r(x) + p(x)*q(x)*r'(x)#

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