What is the first derivative of a+be^θ ?

The first derivative of a+be^θ is 1

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derivative of a+be^θ

derivative of

a + b e^{θ}

1

Solution steps

\frac{d}{d a} (a + b e^{θ})

Treat

b, θ

as constants

Apply the Sum/Difference Rule:

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

= \frac{d a}{d a} + \frac{d}{d a} (b e^{θ})

\frac{d a}{d a} = 1

\frac{d}{d a} (b e^{θ}) = 0

= 1 + 0

Simplify

= 1

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