$$y=8^{\frac{x^2}{\cos x}}$$

$$y=8^{g\left(x\right)}$$

$$g\left(x\right)=\frac{x^2}{cosx}$$

$$g\left(x\right)=\frac{u}{v}\Rightarrow u=x^2 ; v=cosx$$

$$g^{\text{'}}=\frac{u^{\text{'}}v-u{v}^{\text{'}}}{v^2}$$

$$u^{\text{'}}=2x ; v^{\text{'}}=-sin x$$

$$g^{\text{'}}=\frac{2x·cosx-x^2·\left(-sinx\right)}{co{s}^{2}x}$$

$$g^{\text{'}}=\frac{2x·cosx+x^2·\sin x}{co{s}^{2}x}$$

$$y=8^{g\left(x\right)}$$

$$y^{\text{'}}=8^{g\left(x\right)}\ln 8 ·g^{\text{'}}\left(x\right)$$

$$y^{\text{'}}=8^{\frac{x^2}{\cos x}}·\ln 8·\frac{2x·\cos x+x^2·\sin x}{{\cos }^{2}x}$$