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Popular >

derivative of f(x)=2x^4e^x

Solution

derivative of

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

Solution

2 (4 x^{3} e^{x} + e^{x} x^{4})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = e^{x}

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 2 (4 x^{3} e^{x} + e^{x} x^{4})

Popular Examples

integral of (x^3)/3-(5x^2)/2+6x+C

\int \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C d x

integral of 1/(200+3t)

\int \frac{1}{200 + 3 t} d t

sum from n=3 to infinity of 4/(n^2-1)

n = 3 \sum \infty \frac{4}{n ^{2} - 1}

limit as x approaches 0 of-3e^{3x}

x \to 0 lim (- 3 e^{3 x})

integral of xe^{-x/4}

\int x e^{- \frac{x}{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=2x^4e^x ?
The derivative of f(x)=2x^4e^x is 2(4x^3e^x+e^xx^4)
What is the first derivative of f(x)=2x^4e^x ?
The first derivative of f(x)=2x^4e^x is 2(4x^3e^x+e^xx^4)