What is the derivative of x/y+e^y ?

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

What is the first derivative of x/y+e^y ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\int 5^{x} - sec^{2} (x) d x

- x^{2} - 1, x^{2} + 4, [- 2, 3]

y^{^{'}} = x (1 + y)

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

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