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

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

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

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

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

Solution steps

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

Treat

t

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{'}} = \frac{2 x}{y + 1}

\frac{d}{d x} (arcsech (x))

\frac{d}{d x} (\frac{1}{a + b \cdot ( \frac{x}{d} ) ^{c}})

\frac{d y}{d t} + 5 y = 80, y (1) = 100

\frac{d}{d x} (- x + 1)

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