What is the derivative of (x+ae^{2x}+b) ?

The derivative of (x+ae^{2x}+b) is e^{2x}+2e^{2x}(x+a)

What is the first derivative of (x+ae^{2x}+b) ?

The first derivative of (x+ae^{2x}+b) is e^{2x}+2e^{2x}(x+a)

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

e^{2 x} + 2 e^{2 x} (x + a)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{2 x} + 2 e^{2 x} (x + a) + 0

Simplify

= e^{2 x} + 2 e^{2 x} (x + a)

\int 7 16 - 2 x d x

4 x, x^{2} - 5, [- 2.2, 0]

\int 30 x (x + 1)^{4} d x

\frac{d}{d x} (6 x^{2} - 10 x)

\frac{d}{d x} ((x^{4} + 2)^{2} (x^{5} + 4)^{4})

What is the derivative of (x+ae^{2x}+b) ?
The derivative of (x+ae^{2x}+b) is e^{2x}+2e^{2x}(x+a)
What is the first derivative of (x+ae^{2x}+b) ?
The first derivative of (x+ae^{2x}+b) is e^{2x}+2e^{2x}(x+a)