Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 7 \sin{\left(x \right)} \sin{\left(y \right)} + 7 \cos{\left(x \right)} \cos{\left(y \right)}=-26$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 7 y' \sin{\left(x \right)} \cos{\left(y \right)} - 7 y' \sin{\left(y \right)} \cos{\left(x \right)} - 7 \sin{\left(x \right)} \cos{\left(y \right)} - 7 \sin{\left(y \right)} \cos{\left(x \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = -1$