What is the derivative of (2^x/(e^x)) ?

The derivative of (2^x/(e^x)) is (ln(2)-1)(2/e)^x

What is the first derivative of (2^x/(e^x)) ?

The first derivative of (2^x/(e^x)) is (ln(2)-1)(2/e)^x

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\frac{d}{d x} (\frac{2 ^{x}}{e ^{x}})

(ln (2) - 1) (\frac{2}{e})^{x}

Solution steps

\frac{d}{d x} (\frac{2 ^{x}}{e ^{x}})

Simplify

\frac{2 ^{x}}{e ^{x}} : (\frac{2}{e})^{x}

= \frac{d}{d x} ((\frac{2}{e})^{x})

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= (\frac{2}{e})^{x} ln (\frac{2}{e})

Simplify

ln (\frac{2}{e}) : ln (2) - 1

= (ln (2) - 1) (\frac{2}{e})^{x}

y^{^{'}} = y (y - 1)

f (x) = \frac{4 x + 3}{x + 1}, at x = 3

\frac{d}{d x} ((arcsec (\frac{x ^{2}}{2}))^{3 x})

f (x) = - \frac{x}{2}

x + 5

What is the derivative of (2^x/(e^x)) ?
The derivative of (2^x/(e^x)) is (ln(2)-1)(2/e)^x
What is the first derivative of (2^x/(e^x)) ?
The first derivative of (2^x/(e^x)) is (ln(2)-1)(2/e)^x