What is the derivative of 2xe^{6x}+e^{6x}*6x^2 ?

The derivative of 2xe^{6x}+e^{6x}*6x^2 is 36e^{6x}x^2+24e^{6x}x+2e^{6x}

What is the first derivative of 2xe^{6x}+e^{6x}*6x^2 ?

The first derivative of 2xe^{6x}+e^{6x}*6x^2 is 36e^{6x}x^2+24e^{6x}x+2e^{6x}

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

36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 (e^{6 x} + 6 e^{6 x} x) + 6 (e^{6 x} \cdot 6 x^{2} + 2 x e^{6 x}) : 36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

= 36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

\int 2 x^{2} sin (x) d x

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

\int 3 tan^{2} (x) sec^{3} (x) d x

\frac{d}{d x} (ln x^{2} + 9)

x \to - 1 lim (\frac{1}{x})

What is the derivative of 2xe^{6x}+e^{6x}*6x^2 ?
The derivative of 2xe^{6x}+e^{6x}*6x^2 is 36e^{6x}x^2+24e^{6x}x+2e^{6x}
What is the first derivative of 2xe^{6x}+e^{6x}*6x^2 ?
The first derivative of 2xe^{6x}+e^{6x}*6x^2 is 36e^{6x}x^2+24e^{6x}x+2e^{6x}