What is the derivative of a(2xe^{3x}+e^{3x}*3x^2) ?

The derivative of a(2xe^{3x}+e^{3x}*3x^2) is a(9e^{3x}x^2+12e^{3x}x+2e^{3x})

What is the first derivative of a(2xe^{3x}+e^{3x}*3x^2) ?

The first derivative of a(2xe^{3x}+e^{3x}*3x^2) is a(9e^{3x}x^2+12e^{3x}x+2e^{3x})

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\frac{d}{d x} (a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}))

a (9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x})

Solution steps

\frac{d}{d x} (a (2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}))

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= a (2 (e^{3 x} + 3 e^{3 x} x) + 3 (e^{3 x} \cdot 3 x^{2} + 2 x e^{3 x}))

Expand

2 (e^{3 x} + 3 e^{3 x} x) + 3 (e^{3 x} \cdot 3 x^{2} + 2 x e^{3 x}) : 9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x}

= a (9 e^{3 x} x^{2} + 12 e^{3 x} x + 2 e^{3 x})

\int 8 sin^{2} (π x) cos^{5} (π x) d x

(x^{2} sin (x) + 4 y) d x + (x) d y = 0

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

ln (sec (x) + tan (x))

\int 1 + 9 sin^{2} (3 x) d x

What is the derivative of a(2xe^{3x}+e^{3x}*3x^2) ?
The derivative of a(2xe^{3x}+e^{3x}*3x^2) is a(9e^{3x}x^2+12e^{3x}x+2e^{3x})
What is the first derivative of a(2xe^{3x}+e^{3x}*3x^2) ?
The first derivative of a(2xe^{3x}+e^{3x}*3x^2) is a(9e^{3x}x^2+12e^{3x}x+2e^{3x})