What is the derivative of (Ax^2+Bx+Ce^{3x}) ?

The derivative of (Ax^2+Bx+Ce^{3x}) is (2Ax+B)e^{3x}+e^{3x}*3(Ax^2+Bx+C)

What is the first derivative of (Ax^2+Bx+Ce^{3x}) ?

The first derivative of (Ax^2+Bx+Ce^{3x}) is (2Ax+B)e^{3x}+e^{3x}*3(Ax^2+Bx+C)

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\frac{d}{d x} ((A x^{2} + B x + C) e^{3 x})

(2 A x + B) e^{3 x} + e^{3 x} \cdot 3 (A x^{2} + B x + C)

Solution steps

\frac{d}{d x} ((A x^{2} + B x + C) e^{3 x})

Treat

A, B, C

as constants

Apply the Product Rule:

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

f = A x^{2} + B x + C, g = e^{3 x}

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

\frac{d}{d x} (A x^{2} + B x + C) = 2 A x + B

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

= (2 A x + B) e^{3 x} + e^{3 x} \cdot 3 (A x^{2} + B x + C)

\frac{d y}{d x} = x e^{- 2 x}

\int \frac{2}{x + 3} d x

\frac{d}{d x} (\frac{x ^{2} + 3}{( x - 1 ) ^{3} + ( x + 1 ) ^{3}})

(6, - 5), (2, 3)

What is the derivative of (Ax^2+Bx+Ce^{3x}) ?
The derivative of (Ax^2+Bx+Ce^{3x}) is (2Ax+B)e^{3x}+e^{3x}*3(Ax^2+Bx+C)
What is the first derivative of (Ax^2+Bx+Ce^{3x}) ?
The first derivative of (Ax^2+Bx+Ce^{3x}) is (2Ax+B)e^{3x}+e^{3x}*3(Ax^2+Bx+C)