What is (\partial)/(\partial x)(1/(x+3)) ?

The answer to (\partial)/(\partial x)(1/(x+3)) is -1/((x+3)^2)

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(\partial)/(\partial x)(1/(x+3))

\frac{\partial}{\partial x} (\frac{1}{x + 3})

- \frac{1}{( x + 3 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x + 3})

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((x + 3)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 3 ) ^{2}} \frac{\partial}{\partial x} (x + 3)

= - \frac{1}{( x + 3 ) ^{2}} \frac{\partial}{\partial x} (x + 3)

\frac{\partial}{\partial x} (x + 3) = 1

= - \frac{1}{( x + 3 ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( x + 3 ) ^{2}}

x \to 0 lim (x^{2} - 1)

\frac{\partial}{\partial x} (21 x y e^{- x^{2} - y^{2}})

\int e^{5 x} e^{5 x} + 4 d x

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

\int \frac{tan ^{5} ( x )}{sec ( x )} d x

What is (\partial)/(\partial x)(1/(x+3)) ?
The answer to (\partial)/(\partial x)(1/(x+3)) is -1/((x+3)^2)