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Popular >

derivative of Ax^2e^{2x}

Solution

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

Solution

A (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

integral of e^x-x^{2/5}

\int e^{x} - x^{\frac{2}{5}} d x

inverse oflaplace 3/(2s+1)*1/s inverse laplace

\frac{3}{2 s + 1} \cdot \frac{1}{s}

derivative of (x-1/x ^2)

\frac{d}{d x} ((x - \frac{1}{x})^{2})

limit as t approaches x/2 of (sin(t))/t

t \to \frac{x}{2} lim (\frac{sin ( t )}{t})

slope of (-3.5)(4.3)slope

(- 3.5) (4.3)

Frequently Asked Questions (FAQ)

What is the derivative of Ax^2e^{2x} ?
The derivative of Ax^2e^{2x} is A(2xe^{2x}+e^{2x}*2x^2)
What is the first derivative of Ax^2e^{2x} ?
The first derivative of Ax^2e^{2x} is A(2xe^{2x}+e^{2x}*2x^2)