SOLUTION: If f(7)=-5, g(7)=2, f'(7)=3, and g'(7)=-1, find (2f.3g)'(7). Show your calculation.

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Question 1121043: If f(7)=-5, g(7)=2, f'(7)=3, and g'(7)=-1, find (2f.3g)'(7). Show your calculation.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Unless you are using some nonstandard notation, the value of (2f.3g)'(7) is just

(2*f'(7))*(3*g'(7)) = (2(3))*(3(-1)) = 6(-3) = -18

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Yes; thanks, tutor ikleyn. I did not recognize the notation as the derivative of a product.

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
If f(7) = -5, g(7) = 2, f'(7) = 3, and g'(7) = -1, find (2f.3g)'(7). Show your calculation.
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The correct solution is  THIS:


(2f.3g)'(7) = 2f'(7)*3g(7) + 2f(7)*3g'(7) = (2*3)*(3*2) + (2*(-5))*(3*(-1)) = 66.


It uses standard formula for derivative of a product


(u*v)' = u'*v + u*v'.

The tutor @greenestamps misread the problem and inadvertently gave incorrect solution.


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