What is (\partial)/(\partial x)(1/(x+2)) ?

The answer to (\partial)/(\partial x)(1/(x+2)) is -1/((x+2)^2)

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(\partial)/(\partial x)(1/(x+2))

\frac{\partial}{\partial x} (\frac{1}{x + 2})

- \frac{1}{( x + 2 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x + 2})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + 2) = 1

= - \frac{1}{( x + 2 ) ^{2}} \cdot 1

Simplify

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

h \to 0 lim (\frac{( 3 + h ) ^{3} - 9}{h})

\frac{\partial}{\partial x} (3 x^{2} - 4 x y + x yz)

y^{^{'}} = x^{2} - 2

\frac{1}{x + 4}, at x = 5

ln (x^{3} + 2 x^{2} + 2 x)

What is (\partial)/(\partial x)(1/(x+2)) ?
The answer to (\partial)/(\partial x)(1/(x+2)) is -1/((x+2)^2)