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Popular >

derivative of ax^2e^{3x}

Solution

\frac{d}{d x} (a x^{2} e^{3 x})

Solution

a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2})

Solution steps

\frac{d}{d x} (a x^{2} e^{3 x})

Take the constant out:

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

= a \frac{d}{d x} (x^{2} e^{3 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{3 x}

= a (\frac{d}{d x} (x^{2}) e^{3 x} + \frac{d}{d x} (e^{3 x}) x^{2})

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

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

= a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2})

Popular Examples

integral of 2cos(x)cos(2x)

\int 2 cos (x) cos (2 x) d x

derivative of arctan(0)

\frac{d}{d x} (arctan (0))

(\partial)/(\partial y)(x/(x+y))

\frac{\partial}{\partial y} (\frac{x}{x + y})

(\partial)/(\partial y)(-1/4 (y^2+x^2))

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

limit as x approaches-5 of (x+3)/(x+5)

x \to - 5 lim (\frac{x + 3}{x + 5})

Frequently Asked Questions (FAQ)

What is the derivative of ax^2e^{3x} ?
The derivative of ax^2e^{3x} is a(2xe^{3x}+e^{3x}*3x^2)
What is the first derivative of ax^2e^{3x} ?
The first derivative of ax^2e^{3x} is a(2xe^{3x}+e^{3x}*3x^2)