Question

Find the slope of the graph y=x^9-2x+(square root of 5-x)^3 @ (1,7)

Answer 1

That would be the value of dy/dx at y = 1.

You probably meant
y =x^9 -2x +sqrt[(5-x)^3]
= x^9 -2x +(5-x)^(3/2)

Differentiate the function and plug in 1 for x.

dy/dx = 9x^8 -2 -(3/2)*sqrt(5-x)