The value of differentiation of x^7 + 1 w.r.t x^6 is :

$y=x^7+1.$

$u=x^6.$

$\frac{dy}{dx}=7x^6.$

$\frac{du}{dx}=6x^5.$

$\frac{dy}{du}=\frac{\frac{dy}{dx}}{\frac{du}{dx}}=\frac{7x^6}{6x^5}.$

$\frac{dy}{d(x^6)}=\frac{7}{6}x.$

$\frac{d(x^7+1)}{d(x^6)}=\frac{7x}{6}.$