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

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

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

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

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derivative of

y = (\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 - 4 ln (x^{2} - 1) d x

n = 1 \sum \infty n (1)^{n}

7 x^{2} + 8 x

\int \frac{x ^{2}}{x ^{2} + 4 x - 12} d x

\int (8 x^{3} + \frac{1}{2 x ^{2}}) d x

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