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Popular >

derivative of (x+ae^{2x})

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + a, g = e^{2 x}

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

\frac{d}{d x} (x + a) = 1

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

= 1 \cdot e^{2 x} + e^{2 x} \cdot 2 (x + a)

Simplify

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

Graph

Popular Examples

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\int_{0}^{4} x e^{x} d x

d/(dt)((t^3)/6+(t^2)/4+1/2 t)

\frac{d}{d t} (\frac{t ^{3}}{6} + \frac{t ^{2}}{4} + \frac{1}{2} t)

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\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 7} d x

d/(dθ)(-2sin(θ))

\frac{d}{d θ} (- 2 sin (θ))

laplacetransform e^tsin(t)laplace transform

e^{t} sin (t)

Frequently Asked Questions (FAQ)

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