De^x dx=e^x dy dx for some common functions [ y amp; dy dx amp; y amp; dy dx; x^n ...

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Basic Differentiation Rule

If y=ex find ...

Question

If $y = e^{x} f i n d \frac{d y}{d x}$

$e^{x}$

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$\frac{e}{x}$

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$x e^{x - 1}$

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none of these

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Solution

The correct option is A
$e^{x}$

$\frac{d e^{x}}{d x} = e^{x}$
$\frac{d y}{d x}$ for some common functions
$\begin{matrix} y & \frac{d y}{d x} & y & \frac{d y}{d x} x^{n} & n x^{n - 1} & s e c x & s e c x t a n x s i n x & c o s x & c o s e c x & - c o s e c x c o t x c o s x & - s i n x & l n x & \frac{1}{x} t a n x & s e c^{2} x & e^{x} & e^{x} c o t x & - c o s e c^{2} x \end{matrix}$

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Similar questions

Find $\frac{d y}{d x}$ if $y = e^{x} s i n x$

x y = e^{x - y}, find \frac{d y}{d x}

x^{y} = e^{x - y}

\frac{d y}{d x}

x = 1

e^{x} + e^{y} = e^{x + y}

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

If e^{x} + e^{y} = e^{x + y}, prove that \frac{d y}{d x} = - \frac{e^{x} (e^{y} - 1)}{e^{y} (e^{x} - 1)} or \frac{d y}{d x} + e^{y - x} = 0

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