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Popular >

derivative of (x+ae^{3x}+b)

Solution

\frac{d}{d x} ((x + a) e^{3 x} + b)

Solution

e^{3 x} + 3 e^{3 x} (x + a)

Solution steps

\frac{d}{d x} ((x + a) e^{3 x} + b)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} ((x + a) e^{3 x}) + \frac{d b}{d x}

\frac{d}{d x} ((x + a) e^{3 x}) = e^{3 x} + 3 e^{3 x} (x + a)

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

= e^{3 x} + 3 e^{3 x} (x + a) + 0

Simplify

= e^{3 x} + 3 e^{3 x} (x + a)

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Frequently Asked Questions (FAQ)

What is the derivative of (x+ae^{3x}+b) ?
The derivative of (x+ae^{3x}+b) is e^{3x}+3e^{3x}(x+a)
What is the first derivative of (x+ae^{3x}+b) ?
The first derivative of (x+ae^{3x}+b) is e^{3x}+3e^{3x}(x+a)