# How do you find the partial derivative of the function f(x,y)=intcos(-7t^2-6t-1)dt?

You need to be more specific about how $f$ depends on $x$ and $y$. Are they in the limits of the integral? Are they part of the integrand function? As you wrote it, there's no $x$ or $y$ dependence on the right-hand side and the derivatives with respect to $x$ and $y$ would be zero.