Using chain rule, we have...
u = 7x^4 + 3x²
du/dx = 28x³ + 6x
y = √u = u^(½)
dy/du = 1/(2√u)
So we have...
f'(x) = dy/du * du/dx
= 1/(2√u) * (28x³ + 6x)
= (14x³ + 3x)/√(7x^4 + 3x²)
Good luck!
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Verified answer
Using chain rule, we have...
u = 7x^4 + 3x²
du/dx = 28x³ + 6x
y = √u = u^(½)
dy/du = 1/(2√u)
So we have...
f'(x) = dy/du * du/dx
= 1/(2√u) * (28x³ + 6x)
= (14x³ + 3x)/√(7x^4 + 3x²)
Good luck!