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Popular >

derivative of axe^{bx}

Solution

\frac{d}{d x} (a x 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 (1/(x^4))

\int (\frac{1}{x ^{4}}) d x

sum from n=0 to infinity}((-4)^{3n of)/(5^{n-1)}

n = 0 \sum \infty \frac{( - 4 ) ^{3 n}}{5 ^{n - 1}}

(\partial)/(\partial x)(e^{8x+3y})

\frac{\partial}{\partial x} (e^{8 x + 3 y})

integral of [ 1/((4+x^2))]

\int [\frac{1}{( 4 + x ^{2} )}] d x

tangent of y=2x^3,(-3,-54)tangent of

y = 2 x^{3}, (- 3, - 54)

Frequently Asked Questions (FAQ)

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