What is the derivative of Ax^2e^x+Bxe^x+Ce^x ?

The derivative of Ax^2e^x+Bxe^x+Ce^x is A(2xe^x+e^xx^2)+B(e^x+e^xx)+Ce^x

What is the first derivative of Ax^2e^x+Bxe^x+Ce^x ?

The first derivative of Ax^2e^x+Bxe^x+Ce^x is A(2xe^x+e^xx^2)+B(e^x+e^xx)+Ce^x

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

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

Solution steps

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

Treat

A, B, C

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (C e^{x}) = C e^{x}

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

\int \frac{1}{10 x} d x

d er i v a t i v e y^{2}

f^{^{'}} (x) = 3 arctan (x^{2} - 3 x + 2)

\int \frac{sin ( 2 x )}{cos ^{3} ( 2 x )} d x

d er i v a t i v e f (z) = (9 z^{4} + 3 z^{2} + 1) (3 z^{3} - z)

What is the derivative of Ax^2e^x+Bxe^x+Ce^x ?
The derivative of Ax^2e^x+Bxe^x+Ce^x is A(2xe^x+e^xx^2)+B(e^x+e^xx)+Ce^x
What is the first derivative of Ax^2e^x+Bxe^x+Ce^x ?
The first derivative of Ax^2e^x+Bxe^x+Ce^x is A(2xe^x+e^xx^2)+B(e^x+e^xx)+Ce^x