F(x) = sqrt{4x^{2}+3x+5}

Question

find f' please explain?

Answer 1

The function f(x) = √(4x² + 3x + 5)

Differentiating on each side with respect to x.

Recall the formulae: d/dx(√x) = 1/2√x

d/dx(xⁿ) = nx^n-1

d/dx (x) = 1

d/dx(constant) = 0.

Apply chain rule in derivatives.

f'(x) = 1/2[√(4x² + 3x + 5)] d/dx(4x² + 3x + 5)

f'(x) = {1/2[√(4x² + 3x + 5)]} (8x + 3)

f'(x) = (8x + 3)/2[√(4x² + 3x + 5)].