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Popular >

derivative of 1/((x+y))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

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

Simplify

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

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

Popular Examples

limit as x approaches+0+of (1+x)^{(1/x)}

x \to + 0 + lim ((1 + x)^{(\frac{1}{x})})

(dy)/(dx)=1+sqrt(y-x)

\frac{d y}{d x} = 1 + y - x

tangent of 3x^2-6x-9,\at x=3 tangent of

3 x^{2} - 6 x - 9, at x = 3

(\partial)/(\partial y)((xy^2)/(x^2y^3+1))

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

limit as x approaches 1 of (x+3)/(x-2)

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

Frequently Asked Questions (FAQ)

What is the derivative of 1/((x+y)) ?
The derivative of 1/((x+y)) is -(1+\frac{dy)/(dx)}{(x+y)^2}
What is the first derivative of 1/((x+y)) ?
The first derivative of 1/((x+y)) is -(1+\frac{dy)/(dx)}{(x+y)^2}