For 2nd question:
First find f(x):
f(x)=(g⋅h)(x)=g(x)⋅h(x)=(18x)(14x3)
Then find f '(x):
In this case we use product rule:
f′(x)=(18x)′(14x3)+(18x)(14x3)′=14ln18⋅18x⋅x3+18x⋅42x2
Let us call the part before plus sign (1) and the part after plus sign (2)
Differentiate (1):
(1)′=14ln18((18x)′(x3)+(18x)(x3)′)=14ln18(x3⋅18xln18+3⋅18x⋅x2)
Differentiate (2):
(2)′=(18x)′(42x2)+(18x)(42x2)′=42ln18⋅18x⋅x2+84⋅18x⋅x
Add up (1)' and (2)'
z(x)=(1)′+(2)′=14ln18(x3⋅18xln18+3⋅18x⋅x2)+42ln18⋅18x⋅x2+84⋅18x⋅x=14x218xln18(x+3)+42x⋅18x(xln18+2)
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