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Popular >

derivative of (Ax^2+Bx+Ce^x)

Solution

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

Solution

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

Solution steps

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

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

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

Popular Examples

derivative of 3sqrt(x-4)

\frac{d}{d x} (3 x - 4)

limit as x approaches infinity of (e^{3x-8})/(5x)

x \to \infty lim (\frac{e ^{3 x - 8}}{5 x})

integral of (-x+3)

\int (- x + 3) d x

(\partial)/(\partial x)(arctan(z/x))

\frac{\partial}{\partial x} (arctan (\frac{z}{x}))

y^{''}-10y^'+50y=0,y(0)=5,y^'(0)=-2

y^{^{''}} - 10 y^{^{'}} + 50 y = 0, y (0) = 5, y^{^{'}} (0) = - 2

Frequently Asked Questions (FAQ)

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