What is the derivative of (1/2)^{x-1}+3 ?

The derivative of (1/2)^{x-1}+3 is -ln(2)(1/2)^{x-1}

What is the first derivative of (1/2)^{x-1}+3 ?

The first derivative of (1/2)^{x-1}+3 is -ln(2)(1/2)^{x-1}

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derivative of

(\frac{1}{2})^{x - 1} + 3

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((\frac{1}{2})^{x - 1}) + \frac{d}{d x} (3)

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

\frac{d}{d x} (3) = 0

= - ln (2) (\frac{1}{2})^{x - 1} + 0

Simplify

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

What is the derivative of (1/2)^{x-1}+3 ?
The derivative of (1/2)^{x-1}+3 is -ln(2)(1/2)^{x-1}
What is the first derivative of (1/2)^{x-1}+3 ?
The first derivative of (1/2)^{x-1}+3 is -ln(2)(1/2)^{x-1}