A) Given that y=(x^2 +7)^(1/2) find dy/dx
Let x^2 + 7 = m
And we can write
dy/dx = dy/dm * dm/dx
So we have
y = m^(1/2) taking the derivative of this =
dy/dm = (1/2)m^(-1/2)
And
dm/dx = 2x
So...puting this all together, we have
dy/dx = dy/dm * dm/dx = (1/2)m^(-1/2) * 2x = (1/2)(x^2 + 7)^(-1/2) * 2x = x * (x^2 + 7)^(-1/2)