What is the derivative of f(x)=x^2e^{6x} ?

The derivative of f(x)=x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2

What is the first derivative of f(x)=x^2e^{6x} ?

The first derivative of f(x)=x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2

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derivative of

f (x) = x^{2} e^{6 x}

2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{6 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{6 x}

= \frac{d}{d x} (x^{2}) e^{6 x} + \frac{d}{d x} (e^{6 x}) x^{2}

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}

\frac{d}{d x} (cos (x) - 4 tan (x))

\frac{d}{d x} (x arctan (x))

2 y^{^{''}} - y^{^{'}} + 3 y = 0

x^{2} y^{^{''}} - 14 x y^{^{'}} + 56 y = 0

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

What is the derivative of f(x)=x^2e^{6x} ?
The derivative of f(x)=x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2
What is the first derivative of f(x)=x^2e^{6x} ?
The first derivative of f(x)=x^2e^{6x} is 2xe^{6x}+e^{6x}*6x^2