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jubateee

Answered question

2021-12-10

Find the derivatives of the following function f(x) from the first principles

x^{2} + y^{2} = 64

Answer & Explanation

Louis Page

Beginner2021-12-11Added 34 answers

Step 1
Given

x^{2} + y^{2} = 64

Step 2
differentiating wrt "x"

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (64)

\frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) = \frac{d}{d x} (64)

2 x + 2 y \frac{d y}{d x} = 0

2 y \frac{d y}{d x} = 0

2 y \frac{d y}{d x} = - 2 x

\frac{d y}{d x} = - \frac{x}{y}

∴ \frac{d y}{d x} = - \frac{x}{y}

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