Answer this question and show the steps. sqrt{x}+sqrt{y}=3, find the value of frac{dy}{dx} at the point (4,1)

melodykap 2020-12-24 Answered
Answer this question and show the steps. x+y=3, find the value of dydx at the point (4,1)
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crocolylec
Answered 2020-12-25 Author has 100 answers
Step 1 Consider the given function x+y=3 Step 2 Differentiate implicitly with respect to x. ddx(x+y)=ddx(3)
ddx(x12)+ddx(y12)=0
12x121+(12y121)dydx=0
12x12+(12y12)dydx=0
12x+12ydydx=0
dydx=yx=yx Step 3 Now, find the value of dydx at the point (4, 1) dydx(x,y)=(4,1)=14=12 The answer is 12 or -0.5(in decimals).
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