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Popular >

derivative of 4x^2e^x

Solution

derivative of

4 x^{2} e^{x}

Solution

4 (2 x e^{x} + e^{x} x^{2})

Solution steps

\frac{d}{d x} (4 x^{2} e^{x})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{2} e^{x})

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (x^{2}) e^{x} + \frac{d}{d x} (e^{x}) x^{2})

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

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

= 4 (2 x e^{x} + e^{x} x^{2})

Popular Examples

integral of 1/(sqrt(x)+x\sqrt{x)}

\int \frac{1}{x + x x} d x

integral from 1 to x of 1/t

\int_{1}^{x} \frac{1}{t} d t

derivative of x^{6x}derivative of

x^{6 x}

derivative of (x^3)/3+x^2+4x-10 derivative of

\frac{x ^{3}}{3} + x^{2} + 4 x - 10

derivative of (3x^2/((x^2+x)^3))

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

Frequently Asked Questions (FAQ)

What is the derivative of 4x^2e^x ?
The derivative of 4x^2e^x is 4(2xe^x+e^xx^2)
What is the first derivative of 4x^2e^x ?
The first derivative of 4x^2e^x is 4(2xe^x+e^xx^2)