Compute the derivative, dy/dx (use the chain rule):
y = 10/(1 + e ⁻ˣ) = 10 (1 + e ⁻ˣ)⁻¹
===> dy/dx = -10 (1 + e ⁻ˣ)⁻² (-e ⁻ˣ) = 10e ⁻ˣ/(1 + e ⁻ˣ)²
Evaluate the derivative for x = 0 to get the slope of the tangent to the curve at (0, 5) :
dy/dx (0) = 10e ⁰/(1 + e ⁰)² = 10/(1 + 1)² = 10/4 = 5/2
Use the point-slope formula to get the equation of the tangent line:
y - 5 = 5/2 (x - 0)
===> y = 5/2 x + 5
