What is the derivative of f(x)=(1/2)^x ?

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

What is the first derivative of f(x)=(1/2)^x ?

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

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derivative of

f (x) = (\frac{1}{2})^{x}

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

Solution steps

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

Apply the derivative exponent rule:

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

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

Simplify

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

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

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