What is the derivative of ae^x+b ?

The derivative of ae^x+b is ae^x

What is the first derivative of ae^x+b ?

The first derivative of ae^x+b is ae^x

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

a e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d b}{d x} = 0

= a e^{x} + 0

Simplify

= a e^{x}

\frac{\partial}{\partial y} (x y e^{- 2 y})

y^{^{'''}} - 2 y^{^{''}} - 48 y^{^{'}} = 0

\frac{\partial}{\partial x} (x^{2} - 3 y^{2} + 7)

y^{^{'}} + y = 5

\frac{70}{x}