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Popular >

derivative of y=x^4e^{3x}

Solution

derivative of

y = x^{4} e^{3 x}

Solution

4 x^{3} e^{3 x} + e^{3 x} \cdot 3 x^{4}

Solution steps

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

Apply the Product Rule:

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

f = x^{4}, g = e^{3 x}

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

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 4 x^{3} e^{3 x} + e^{3 x} \cdot 3 x^{4}

Graph

Popular Examples

sum from n=5 to infinity of 1/(n^2+n)

n = 5 \sum \infty \frac{1}{n ^{2} + n}

integral from 0 to pi/3 of cos(4x)

\int_{0}^{\frac{π}{3}} cos (4 x) d x

sum from n=1 to infinity}(-1)^{n+1 of 2/(n+1)

n = 1 \sum \infty (- 1)^{n + 1} \frac{2}{n + 1}

derivative of y=8xe^x derivative of

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d/(dz)((2z^6+2)/(1z^2+5))

\frac{d}{d z} (\frac{2 z ^{6} + 2}{1 z ^{2} + 5})

Frequently Asked Questions (FAQ)

What is the derivative of y=x^4e^{3x} ?
The derivative of y=x^4e^{3x} is 4x^3e^{3x}+e^{3x}*3x^4
What is the first derivative of y=x^4e^{3x} ?
The first derivative of y=x^4e^{3x} is 4x^3e^{3x}+e^{3x}*3x^4