What is the derivative of 0.5^x ?

The derivative of 0.5^x is -0.69314…*0.5^x

What is the first derivative of 0.5^x ?

The first derivative of 0.5^x is -0.69314…*0.5^x

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derivative of

0. 5^{x}

- 0.69314 \dots \cdot 0. 5^{x}

Solution steps

\frac{d}{d x} (0. 5^{x})

Apply the derivative exponent rule:

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

= 0. 5^{x} ln (0.5)

Simplify

0. 5^{x} ln (0.5) : - 0.69314 \dots \cdot 0. 5^{x}

= - 0.69314 \dots \cdot 0. 5^{x}

What is the derivative of 0.5^x ?
The derivative of 0.5^x is -0.69314…*0.5^x
What is the first derivative of 0.5^x ?
The first derivative of 0.5^x is -0.69314…*0.5^x