What is the derivative of (1/3 ^x) ?

The derivative of (1/3 ^x) is -ln(3)(1/3)^x

What is the first derivative of (1/3 ^x) ?

The first derivative of (1/3 ^x) is -ln(3)(1/3)^x

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\frac{d}{d x} ((\frac{1}{3})^{x})

- ln (3) (\frac{1}{3})^{x}

Solution steps

\frac{d}{d x} ((\frac{1}{3})^{x})

Apply the derivative exponent rule:

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

= (\frac{1}{3})^{x} ln (\frac{1}{3})

Simplify

(\frac{1}{3})^{x} ln (\frac{1}{3}) : - ln (3) (\frac{1}{3})^{x}

= - ln (3) (\frac{1}{3})^{x}

\int \frac{1}{e ^{x} - 2} d x

y^{^{'}} + t y = t y^{2}

y^{^{''}} - 4 y = \frac{4 x}{e ^{2 x}}

n = 0 \sum \infty \frac{1}{n + e ^{n}}

\frac{d}{d x} (\frac{24}{( x + 2 ) ^{3}})

What is the derivative of (1/3 ^x) ?
The derivative of (1/3 ^x) is -ln(3)(1/3)^x
What is the first derivative of (1/3 ^x) ?
The first derivative of (1/3 ^x) is -ln(3)(1/3)^x