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

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

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

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

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\frac{d}{d x} ((x + a) \cdot 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)

f (x) = 4 sin^{2} (x)

\int - x^{2} d x

\int_{0}^{2} x 4 x^{2} + 9 d x

(e^{- \frac{x ^{2}}{2}})^{^{'}}

\int \frac{7}{1 - x ^{2}} d x

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