What is the derivative of (1/5)^x ?

The derivative of (1/5)^x is -ln(5)(1/5)^x

What is the first derivative of (1/5)^x ?

The first derivative of (1/5)^x is -ln(5)(1/5)^x

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derivative of

(\frac{1}{5})^{x}

- ln (5) (\frac{1}{5})^{x}

Solution steps

\frac{d}{d x} ((\frac{1}{5})^{x})

Apply the derivative exponent rule:

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

= (\frac{1}{5})^{x} ln (\frac{1}{5})

Simplify

(\frac{1}{5})^{x} ln (\frac{1}{5}) : - ln (5) (\frac{1}{5})^{x}

= - ln (5) (\frac{1}{5})^{x}

d er i v a t i v e y = x^{3} + 2 x - 1

d er i v a t i v e a^{\frac{1}{x}}

d er i v a t i v e 3 ln (2 x - 1)

d er i v a t i v e y = x^{2} ln (4 x)

d er i v a t i v e 2^{3} x

What is the derivative of (1/5)^x ?
The derivative of (1/5)^x is -ln(5)(1/5)^x
What is the first derivative of (1/5)^x ?
The first derivative of (1/5)^x is -ln(5)(1/5)^x