What is the derivative of a*e^{2x}+b*e^x+c ?

The derivative of a*e^{2x}+b*e^x+c is be^x+2ae^{2x}

What is the first derivative of a*e^{2x}+b*e^x+c ?

The first derivative of a*e^{2x}+b*e^x+c is be^x+2ae^{2x}

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\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{x} + c)

b e^{x} + 2 a e^{2 x}

Solution steps

\frac{d}{d x} (a e^{2 x} + b e^{x} + c)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a e^{2 x}) + \frac{d}{d x} (b e^{x}) + \frac{d c}{d x}

\frac{d}{d x} (a e^{2 x}) = a e^{2 x} \cdot 2

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

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

= a e^{2 x} \cdot 2 + b e^{x} + 0

Simplify

= b e^{x} + 2 a e^{2 x}

What is the derivative of a*e^{2x}+b*e^x+c ?
The derivative of a*e^{2x}+b*e^x+c is be^x+2ae^{2x}
What is the first derivative of a*e^{2x}+b*e^x+c ?
The first derivative of a*e^{2x}+b*e^x+c is be^x+2ae^{2x}