What is (\partial)/(\partial x)(sqrt(x^2+y^2-4x+5)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-4x+5)) is (x-2)/(sqrt(x^2+y^2-4x+5))

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(\partial)/(\partial x)(sqrt(x^2+y^2-4x+5))

\frac{\partial}{\partial x} (x^{2} + y^{2} - 4 x + 5)

\frac{x - 2}{x ^{2} + y ^{2} - 4 x + 5}

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} - 4 x + 5)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + y ^{2} - 4 x + 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 4 x + 5)

= \frac{1}{2 x ^{2} + y ^{2} - 4 x + 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 4 x + 5)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 4 x + 5) = 2 x - 4

= \frac{1}{2 x ^{2} + y ^{2} - 4 x + 5} (2 x - 4)

Simplify

\frac{1}{2 x ^{2} + y ^{2} - 4 x + 5} (2 x - 4) : \frac{x - 2}{x ^{2} + y ^{2} - 4 x + 5}

= \frac{x - 2}{x ^{2} + y ^{2} - 4 x + 5}

f (x) = 3 x + 7, at x = 3

(x - 8) \cdot \frac{d y}{d x} + y = (x^{2} - 3)

\frac{\partial}{\partial x} (\frac{4 y}{x ^{3}})

n = 0 \sum \infty \infty

\frac{s + 1}{s ^{2} + 2 s + 10}

What is (\partial)/(\partial x)(sqrt(x^2+y^2-4x+5)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+y^2-4x+5)) is (x-2)/(sqrt(x^2+y^2-4x+5))