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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 4 \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}

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

\int - x + tan (x) d x

y = sin (x) - cos (x)

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

y^{^{'}} + 3 y = x e^{- 2 x} + e^{- 3 x}

y^{^{''}} = x (y^{^{'}})^{2}

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