Find the first derivative for g(x) = 3(6 − 9x)^4
A. g′(x) = 108(6 − 9x)^3
B. g′(x) = −12(6 − 9x)^3
C. None of these
D. g′(x) = −108(6 − 9x)^3
E. g′(x) = 12(6 − 9x)^3

Question

Find the first derivative for g(x) = 3(6 − 9x)^4
A. g′(x) = 108(6 − 9x)^3 
B. g′(x) = −12(6 − 9x)^3 
C. None of these
D. g′(x) = −108(6 − 9x)^3 
E. g′(x) = 12(6 − 9x)^3

anonymous · Answer

Its  
D. g′(x) = −108(6 − 9x)^3

anonymous · Answer

$$g(x) = 3(6 − 9x)^4 \rightarrow g'(x) = 3 \times 4 (6 − 9x)^3 \frac{d}{dx}(6 − 9x)$$
$$= 12 (6 − 9x)^3 (-9) = 12(-9) (6 − 9x)^3 = -108 (6 − 9x)^3 $$ Which is the required derivative.

@lesliemariahp

anonymous · Answer

Thank you so much! @dpasingh