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

The derivative of f(x)=4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2

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

The first derivative of f(x)=4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2

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derivative of

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

e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (4 x^{3} e^{x}) = 4 (3 x^{2} e^{x} + e^{x} x^{3})

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

= 4 (3 x^{2} e^{x} + e^{x} x^{3}) + e^{x} x^{4} + 4 x^{3} e^{x}

Simplify

4 (3 x^{2} e^{x} + e^{x} x^{3}) + e^{x} x^{4} + 4 x^{3} e^{x} : e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

= e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

y^{^{'}} + (4 x) y = - 4 x - 9

\frac{d}{d x} (5 x + 4)

\int ((2 x - 1) y^{2} sin (4 x y)) d x

\int 17 x e^{19 x} d x

x \to 0 + lim ((tan (5 x))^{x})

What is the derivative of f(x)=4x^3e^x+e^xx^4 ?
The derivative of f(x)=4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2
What is the first derivative of f(x)=4x^3e^x+e^xx^4 ?
The first derivative of f(x)=4x^3e^x+e^xx^4 is e^xx^4+8e^xx^3+12e^xx^2