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Popular >

derivative of cxe^{3x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= c \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}

= c (\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

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

Simplify

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

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\int ln (11 x) d x

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\int_{- 2}^{- 1} x^{2} e^{x^{3} + 8} d x

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Frequently Asked Questions (FAQ)

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