Hvad er dy / dx af 2xsqrtx?

Hvad er dy / dx af 2xsqrtx?
Anonim

Svar:

# Dy / dx = 3sqrtx #

Forklaring:

# Y = 2xsqrtx = uv #

# Dy / dx = u (dv) / dx + v (du) / dx #

# U = 2x #

# (Du) / dx) = 2 #

# V = sqrtx = x ^ (1/2) #

# (Dv) / (dx) = 1/2 * x ^ (1 / 2-1) = x ^ (- 1/2) / 2 #

# Dy / dx = 2x * x ^ (- 1/2) / 2 + 2 * x ^ (1/2) = sqrtx + 2sqrtx = 3sqrtx #