What is the derivative of f(x)=x^4e^x ?

The derivative of f(x)=x^4e^x is 4x^3e^x+e^xx^4

What is the first derivative of f(x)=x^4e^x ?

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

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derivative of

f (x) = 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}

y = 4 x^{3} - 20 x + 25

\frac{d}{d x} (15 x^{2} - 15 x^{4})

\int \frac{1}{( x - 6 ) ^{2}} d x

\frac{\partial}{\partial x} (sin (x^{2}) + x y^{3})

f (x) = \frac{1 + csc ( x ^{3} )}{1 - cot ( x ^{3} )}

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