Find d/dx for the equation

Question

Find  .

Question options:

1)
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3)
4)

Answer 1

Hi Braxton! the images aren't loading but Wyzant gives text descriptions. Here is what I understood of the text descriptions. Let me know if there's any issues.

1)the square root of the quantity 4 times x plus 1

d/dx[ √(4x+1) ]

(4x+1)^{(1/2 -1)} • d/dx[4x+1] written as fractional power

(4x+1)^(-1/2) • 4

4(4x+1)^(-1/2)

2)the sum of the square root of the quantity 16 times x squared plus 1 and the square root of 2

d/dx[ √(16x²+1) + √2 ]

(16x²+1)^{1/2 -1}•d/dx[ 16x²+1 ] + 0

(16x²+1)^-1/2 •32x

32x (16x²+1)^-1/2

3)the product of 4 and the sqrt of the quantity 16 times x squared plus 1

d/dx[ 4√(16x²+1) ]

4•(16x²+1)^{1/2 -1}•d/dx[ 16x²+1 ]

4•(16x²+1)^-1/2 •32x

128x(16x²+1)^-1/2

4) the square root of the quantity 16 times x squared plus 1

d/dx[ √(16x²+1) ]

(16x²+1)^{1/2 -1}•d/dx[ 16x²+1 ]

(16x²+1)^-1/2 •32x

32x(16x²+1)^-1/2