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Popular >

derivative of axe^{bx}

Solution

\frac{d}{d x} (a \cdot x \cdot e^{b x})

Solution

a (e^{b x} + b e^{b x} x)

Solution steps

\frac{d}{d x} (a x e^{b x})

Take the constant out:

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

= a \frac{d}{d x} (x e^{b x})

Apply the Product Rule:

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

f = x, g = e^{b x}

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

\frac{d x}{d x} = 1

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

= a (1 \cdot e^{b x} + e^{b x} b x)

Simplify

= a (e^{b x} + b e^{b x} x)

Popular Examples

integral of (y-1)/(-y-1)

\int \frac{y - 1}{- y - 1} d y

(\partial)/(\partial y)(2(y+1)e^{2x})

\frac{\partial}{\partial y} (2 (y + 1) e^{2 x})

slope ofintercept (-6,3),(4,-1)slope intercept

(- 6, 3), (4, - 1)

derivative of-19.6x+2 derivative of

- 19.6 x + 2

integral of x\sqrt[4]{x+20}

Frequently Asked Questions (FAQ)

What is the derivative of a*x*e^{bx} ?
The derivative of a*x*e^{bx} is a(e^{bx}+be^{bx}x)
What is the first derivative of a*x*e^{bx} ?
The first derivative of a*x*e^{bx} is a(e^{bx}+be^{bx}x)