What is the derivative of x^3e^{4x} ?

The derivative of x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3

What is the first derivative of x^3e^{4x} ?

The first derivative of x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3

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

3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = e^{4 x}

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

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

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

= 3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

t^{2} y^{^{''}} + 7 t y^{^{'}} + 5 y = t

\frac{d}{d x} (\frac{2}{5} x^{15})

t^{2} cos (2 t + 3 0^{\circ})

f (x) = 5 x sin (π x)

y^{^{''}} - 2 y^{^{'}} + y = e^{x} tan^{- 1} (x)

What is the derivative of x^3e^{4x} ?
The derivative of x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3
What is the first derivative of x^3e^{4x} ?
The first derivative of x^3e^{4x} is 3x^2e^{4x}+e^{4x}*4x^3