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Popular >

derivative of 1/6 xe^{3x}

Solution

\frac{d}{d x} (\frac{1}{6} x e^{3 x})

Solution

\frac{1}{6} (e^{3 x} + 3 e^{3 x} x)

Solution steps

\frac{d}{d x} (\frac{1}{6} x e^{3 x})

Take the constant out:

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

= \frac{1}{6} \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}

= \frac{1}{6} (\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

= \frac{1}{6} (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

Simplify

= \frac{1}{6} (e^{3 x} + 3 e^{3 x} x)

Popular Examples

(\partial)/(\partial x)(1/((1/x+1/y)))

\frac{\partial}{\partial x} \frac{1}{( \frac{1}{x} + \frac{1}{y} )}

integral of (6x^3)/(sqrt(16+x^2))

\int \frac{6 x ^{3}}{16 + x ^{2}} d x

y^{^{'}} = 2 y + x^{2} + 9

derivative of (x+1^{x^2})

\frac{d}{d x} ((x + 1)^{x^{2}})

tangent of f(x)=x^2+ax+2,\at x=1 tangent of

f (x) = x^{2} + a x + 2, at x = 1

Frequently Asked Questions (FAQ)

What is the derivative of 1/6 xe^{3x} ?
The derivative of 1/6 xe^{3x} is 1/6 (e^{3x}+3e^{3x}x)
What is the first derivative of 1/6 xe^{3x} ?
The first derivative of 1/6 xe^{3x} is 1/6 (e^{3x}+3e^{3x}x)