Can someone please help me with the following question?

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1 Answer
Feb 6, 2018

a. #-18#.

b. #-22/25#.

Explanation:

Part a.

#h(x)=f(x)g(x)#.

Then, using the Product Rule for Diffn., we get,

#:. h'(x)=f(x)g'(x)+f'(x)g(x)#.

#:. h'(3)=f(3)g'(3)+f'(3)g(3)#,

#=2*1+(-4)(5)............[because," Given]"#.

# rArr h'(3)=-18#.

Part b.

If, #h(x)=(f(x))/g(x)#, then, using the Quotient Rule, we get,

# h'(x)={g(x)f'(x)-f(x)g'(x)}/[g(x)]^2#,

#:. h'(3)={g(3)f'(3)-f(3)g'(3)}/[g(3)]^2#,

#={5(-4)-2*1}/5^2#.

# rArr h'(x)=-22/25#.