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Popular >

derivative of Axe^{3x}

Solution

\frac{d}{d x} (A x e^{3 x})

Solution

A (e^{3 x} + 3 e^{3 x} x)

Solution steps

\frac{d}{d x} (A x e^{3 x})

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{3 x}

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

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

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

= A (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

Simplify

= A (e^{3 x} + 3 e^{3 x} x)

Popular Examples

f(t)=sin(t)-tcos(t)

f (t) = sin (t) - t cos (t)

f^'(x)=(1-e^x)/(9+e^x)

f^{^{'}} (x) = \frac{1 - e ^{x}}{9 + e ^{x}}

xy^'+y=-2xy^2,y(1)=2

x y^{^{'}} + y = - 2 x y^{2}, y (1) = 2

(\partial)/(\partial y)(y^2sin(xy))

\frac{\partial}{\partial y} (y^{2} sin (x y))

limit as x approaches 5 of 2/((x-5)^6)

x \to 5 lim (\frac{2}{( x - 5 ) ^{6}})

Frequently Asked Questions (FAQ)

What is the derivative of Axe^{3x} ?
The derivative of Axe^{3x} is A(e^{3x}+3e^{3x}x)
What is the first derivative of Axe^{3x} ?
The first derivative of Axe^{3x} is A(e^{3x}+3e^{3x}x)