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Popular >

derivative of axe^{2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

tangent of f(x)=x^3+x^2+(6/x),\at x=1 tangent of

f (x) = x^{3} + x^{2} + (\frac{6}{x}), at x = 1

tangent of y=(x-4)^2,\at x=5 tangent of

y = (x - 4)^{2}, at x = 5

(dy)/(dt)=-2y+10

\frac{d y}{d t} = - 2 y + 10

integral of x^3(x^4-1)^5

\int x^{3} (x^{4} - 1)^{5} d x

tangent of y=4e^xcos(x),(0,4)tangent of

y = 4 e^{x} cos (x), (0, 4)

Frequently Asked Questions (FAQ)

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