What is the derivative of y=e^{8/9 x} ?

The derivative of y=e^{8/9 x} is e^{(8x)/9} 8/9

What is the first derivative of y=e^{8/9 x} ?

The first derivative of y=e^{8/9 x} is e^{(8x)/9} 8/9

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derivative of

y = e^{\frac{8}{9} x}

e^{\frac{8 x}{9}} \frac{8}{9}

Solution steps

\frac{d}{d x} (e^{\frac{8}{9} x})

Simplify

e^{\frac{8}{9} x} : e^{\frac{8 x}{9}}

= \frac{d}{d x} (e^{\frac{8 x}{9}})

Apply the chain rule:

e^{\frac{8 x}{9}} \frac{d}{d x} (\frac{8 x}{9})

= e^{\frac{8 x}{9}} \frac{d}{d x} (\frac{8 x}{9})

\frac{d}{d x} (\frac{8 x}{9}) = \frac{8}{9}

= e^{\frac{8 x}{9}} \frac{8}{9}

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What is the derivative of y=e^{8/9 x} ?
The derivative of y=e^{8/9 x} is e^{(8x)/9} 8/9
What is the first derivative of y=e^{8/9 x} ?
The first derivative of y=e^{8/9 x} is e^{(8x)/9} 8/9