What is the derivative of (2(Ae^x+Bx+C)) ?

The derivative of (2(Ae^x+Bx+C)) is 2(e^xA+B)

What is the first derivative of (2(Ae^x+Bx+C)) ?

The first derivative of (2(Ae^x+Bx+C)) is 2(e^xA+B)

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\frac{d}{d x} ((2) (A e^{x} + B x + C))

2 (e^{x} A + B)

Solution steps

\frac{d}{d x} ((2) (A e^{x} + B x + C))

Treat

A, B, C

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (A e^{x} + B x + C)

Apply the Sum/Difference Rule:

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

= 2 (\frac{d}{d x} (A e^{x}) + \frac{d}{d x} (B x) + \frac{d C}{d x})

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

\frac{d}{d x} (B x) = B

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

= 2 (A e^{x} + B + 0)

Simplify

= 2 (e^{x} A + B)

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What is the derivative of (2(Ae^x+Bx+C)) ?
The derivative of (2(Ae^x+Bx+C)) is 2(e^xA+B)
What is the first derivative of (2(Ae^x+Bx+C)) ?
The first derivative of (2(Ae^x+Bx+C)) is 2(e^xA+B)