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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})

Graph

Popular Examples

x(dy)/(dx)=3xe^x-y+6x^2

x \frac{d y}{d x} = 3 x e^{x} - y + 6 x^{2}

limit as x approaches 1 of x^{4/(1-x)}

x \to 1 lim (x^{\frac{4}{1 - x}})

integral of sqrt(-x^2+25)

\int - x^{2} + 25 d x

y^{''}+3y^'-40y=0

y^{^{''}} + 3 y^{^{'}} - 40 y = 0

integral of (-2)/(t+1)

\int \frac{- 2}{t + 1} d t

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)