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Popular >

derivative of 1/x+1/y

Solution

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

Solution

- \frac{1}{x ^{2}} - \frac{\frac{d y}{d x}}{y ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

y^{''}+(y^')^2=0

y^{^{''}} + (y^{^{'}})^{2} = 0

area 7cos(7x),7-7cos(7x),[0, pi/7 ]area

7 cos (7 x), 7 - 7 cos (7 x), [0, \frac{π}{7}]

5ysqrt(x^2+1)(dy)/(dx)+4x=0

5 y x^{2} + 1 \frac{d y}{d x} + 4 x = 0

derivative of 1/((3x+1^2))

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

derivative of y=ln((x^2)/4)derivative of

y = ln (\frac{x ^{2}}{4})

Frequently Asked Questions (FAQ)

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