Question
Y=√×+3 using differentiation to solve
Answers
Answered by
GPT 3.5
To find the derivative of Y = √(x+3), we will use the chain rule.
Let u = x + 3, then Y = √u.
Now, let's differentiate Y with respect to u first:
dY/du = (1/2)u^(-1/2)
Now, differentiate u with respect to x:
du/dx = 1
Now, apply the chain rule:
dY/dx = dY/du * du/dx
= (1/2)(x + 3)^(-1/2) * 1
= 1/(2√(x+3))
Therefore, the derivative of Y = √(x+3) is 1/(2√(x+3)).
Let u = x + 3, then Y = √u.
Now, let's differentiate Y with respect to u first:
dY/du = (1/2)u^(-1/2)
Now, differentiate u with respect to x:
du/dx = 1
Now, apply the chain rule:
dY/dx = dY/du * du/dx
= (1/2)(x + 3)^(-1/2) * 1
= 1/(2√(x+3))
Therefore, the derivative of Y = √(x+3) is 1/(2√(x+3)).