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Popular >

derivative of x/y+y/x

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

integral from 2 to 4 of (x^2+2)^3

\int_{2}^{4} (x^{2} + 2)^{3} d x

y^{''}+y=t,y(0)=1,y(1)=-2

y^{^{''}} + y = t, y (0) = 1, y (1) = - 2

limit as h approaches 0 of ((3+h)^4-81)/h

h \to 0 lim (\frac{( 3 + h ) ^{4} - 81}{h})

derivative of 1/(2sqrt(x)+1/(8x^{7/8)})

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{8 x ^{\frac{7}{8}}})

laplacetransform e^{-2t}(2cos(3t)-sin(3t))laplace transform

e^{- 2 t} (2 cos (3 t) - sin (3 t))

Frequently Asked Questions (FAQ)

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