What is the derivative of y=x^4e^x ?

The derivative of y=x^4e^x is 4x^3e^x+e^xx^4

What is the first derivative of y=x^4e^x ?

The first derivative of y=x^4e^x is 4x^3e^x+e^xx^4

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derivative of

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

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

Solution steps

\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}

= \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}

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

x \to 5 lim (6)

x^{^{''}} + 2 x^{^{'}} + 4 x = 0

\frac{d}{d z} (\frac{z + i}{z - i})

x \to - 1 lim (3 x^{2} - 2 x^{2} + 4)

e^{3} e^{t} (- sin (π t))

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