What is the derivative of 2^{(x/(20)}) ?

The derivative of 2^{(x/(20)}) is 1/20 ln(2)e^{(ln(2)x)/(20)}

What is the first derivative of 2^{(x/(20)}) ?

The first derivative of 2^{(x/(20)}) is 1/20 ln(2)e^{(ln(2)x)/(20)}

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\frac{d}{d x} (2^{(\frac{x}{20})})

\frac{1}{20} ln (2) e^{\frac{l n ( 2 ) x}{20}}

Solution steps

\frac{d}{d x} (2^{(\frac{x}{20})})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{\frac{x}{20}} = e^{\frac{x}{20} l n (2)}

= \frac{d}{d x} (e^{\frac{x}{20} l n (2)})

Apply the chain rule:

e^{\frac{x}{20} l n (2)} \frac{d}{d x} (\frac{x}{20} ln (2))

= e^{\frac{x}{20} l n (2)} \frac{d}{d x} (\frac{x}{20} ln (2))

\frac{d}{d x} (\frac{x}{20} ln (2)) = \frac{1}{20} ln (2)

= e^{\frac{x}{20} l n (2)} \frac{1}{20} ln (2)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{20} ln (2) e^{\frac{l n ( 2 ) x}{20}}

(1 - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (1 + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

\frac{d ^{2}}{d x ^{2}} ((6 x^{2} + 4)^{6})

x \to \infty lim (- e^{- x})

\frac{d}{d x} (\frac{1}{x ^{2} + y ^{2}})

x \to \infty lim (- 4 e^{x})

What is the derivative of 2^{(x/(20)}) ?
The derivative of 2^{(x/(20)}) is 1/20 ln(2)e^{(ln(2)x)/(20)}
What is the first derivative of 2^{(x/(20)}) ?
The first derivative of 2^{(x/(20)}) is 1/20 ln(2)e^{(ln(2)x)/(20)}