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Popular >

derivative of e^y+y/x

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

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

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

Popular Examples

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

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

derivative of arcsin(8x+arccos(8x))

\frac{d}{d x} (arcsin (8 x) + arccos (8 x))

y^{''}-6y^'-16y=0

y^{^{''}} - 6 y^{^{'}} - 16 y = 0

derivative of 4x^{0.75}*(240-2x^{0.5})

\frac{d}{d x} (4 x^{0.75} \cdot (240 - 2 x)^{0.5})

integral from-3 to-1 of 5/(x^4)

\int_{- 3}^{- 1} \frac{5}{x ^{4}} d x

Frequently Asked Questions (FAQ)

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