Differentiate with respect to 𝑥
a. (7𝑥 – 4 )3
b. √(6𝑥+4)
a. ((7x−4)3)′=3(7x−4)2⋅7=21(7x−4)2\big((7x-4)^3\big)^\prime =3(7x-4)^2\cdot 7=21(7x-4)^2((7x−4)3)′=3(7x−4)2⋅7=21(7x−4)2
b. (6x+4)′=((6x+4)1/2)′=12(6x+4)−1/2⋅6=36x+4\big(\sqrt{6x+4}\big)^\prime =\big((6x+4)^{1/2}\big)^\prime=\tfrac{1}{2}(6x+4)^{-1/2}\cdot 6=\frac{3}{\sqrt{6x+4}}(6x+4)′=((6x+4)1/2)′=21(6x+4)−1/2⋅6=6x+43
Answers: a. 21(7x−4)2;21(7x-4)^2;21(7x−4)2; b. 36x+4.\frac{3}{\sqrt{6x+4}}.6x+43.
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