Answer to Question #346438 in Calculus for bookaddict

Question

Differentiate with respect to 𝑥

a. (7𝑥 – 4 )³

b. √(6𝑥+4)

Answer 1

a. $\big((7x-4)^3\big)^\prime =3(7x-4)^2\cdot 7=21(7x-4)^2$

b. $\big(\sqrt{6x+4}\big)^\prime =\big((6x+4)^{1/2}\big)^\prime=\tfrac{1}{2}(6x+4)^{-1/2}\cdot 6=\frac{3}{\sqrt{6x+4}}$

Answers: a. $21(7x-4)^2;$ b. $\frac{3}{\sqrt{6x+4}}.$