What is the derivative of 2x^5e^x ?

The derivative of 2x^5e^x is 2(5x^4e^x+e^xx^5)

What is the first derivative of 2x^5e^x ?

The first derivative of 2x^5e^x is 2(5x^4e^x+e^xx^5)

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\frac{d}{d x} (2 x^{5} e^{x})

2 (5 x^{4} e^{x} + e^{x} x^{5})

Solution steps

\frac{d}{d x} (2 x^{5} e^{x})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{5} e^{x})

Apply the Product Rule:

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

f = x^{5}, g = e^{x}

= 2 (\frac{d}{d x} (x^{5}) e^{x} + \frac{d}{d x} (e^{x}) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 2 (5 x^{4} e^{x} + e^{x} x^{5})

x \to 0 + lim (x^{2} (1 + ln (x)))

f (x) = \frac{2}{x ^{3}}

cot^{2} (x π)

y = 6 cos (x + y)

y^{^{''}} + 4 y = 2 sec (2 x)

What is the derivative of 2x^5e^x ?
The derivative of 2x^5e^x is 2(5x^4e^x+e^xx^5)
What is the first derivative of 2x^5e^x ?
The first derivative of 2x^5e^x is 2(5x^4e^x+e^xx^5)