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Popular >

derivative of 2x^2e^{2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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

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

Popular Examples

derivative of (x^2)/(1+8x)derivative of

\frac{x ^{2}}{1 + 8 x}

derivative of 2sqrt(x+1)

\frac{d}{d x} (2 x + 1)

integral from-infinity to 0 of e^{8x}

\int_{- \infty}^{0} e^{8 x} d x

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

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

integral of x^2*sin(nx)

\int x^{2} \cdot sin (n x) d x

Frequently Asked Questions (FAQ)

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