Verified answer

C = A√(H² + X²) + B(D - X)

C = A√(H² + X²) + BD - BX

A, B, D, and H are constants:

The derivative of A√(H² + X²) using chain rule => A / 2 * (1 / √(H² + X²)) * (2X)

Derivative of BD => 0

Derivative of -BX = -B

dC / dX = (A * 2x / (2√(H² + X²)) - B

dC / dx = AX / √(H² + X²) - B

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If the variables are confusing you can always plug in appropriate numbers for A, B, H, and D.

Let A = 10

B = 5

H = 4

D = 3

C = A√(H² + X²) + B(D - X)

C = A√(H² + X²) + BD - BX

C = 10√(16 + X²) + 15 - 5X

C' = 1/2(10 * (16 + X²)^(-1/2) * 2X) + 0 - 5

C' = 10X / √(16 + X²) - 5

B = 5

A = 10

H = 4, H² = 16

C' = AX / √(H² + X²) - B