Answer
$$\frac{{dy}}{{dx}} = 21{x^2} - 8x - 5$$
Work Step by Step
$$\eqalign{
& y = 7{x^3} - 4{x^2} - 5x + \sqrt 2 \cr
& {\text{differentiate both sides with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {7{x^3} - 4{x^2} - 5x + \sqrt 2 } \right] \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {7{x^3}} \right] - \frac{d}{{dx}}\left[ {4{x^2}} \right] - \frac{d}{{dx}}\left[ {5x} \right] + \frac{d}{{dx}}\left[ {\sqrt 2 } \right] \cr
& {\text{use the power rule for differentiation }}\frac{d}{{dx}}\left[ {{x^n}} \right] = n{x^{n - 1}}{\text{ and }}\frac{d}{{dx}}\left[ k \right] = 0 \cr
& \frac{{dy}}{{dx}} = 21{x^2} - 8x - 5 + 0 \cr
& \frac{{dy}}{{dx}} = 21{x^2} - 8x - 5 \cr} $$
