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Popular Calculus >

derivative of 8xe^{6x}

Solution

\frac{d}{d x} (8 x e^{6 x})

Solution

8 (e^{6 x} + 6 e^{6 x} x)

Solution steps

\frac{d}{d x} (8 x e^{6 x})

Take the constant out:

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

= 8 \frac{d}{d x} (x e^{6 x})

Apply the Product Rule:

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

f = x, g = e^{6 x}

= 8 (\frac{d x}{d x} e^{6 x} + \frac{d}{d x} (e^{6 x}) x)

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 8 (1 \cdot e^{6 x} + e^{6 x} \cdot 6 x)

Simplify

= 8 (e^{6 x} + 6 e^{6 x} x)

Graph

Popular Examples

derivative of (3x^2-9x+1/(7x+8))

\frac{d}{d x} (\frac{3 x ^{2} - 9 x + 1}{7 x + 8})

integral of (18-18x)/(1-sqrt(x))

\int \frac{18 - 18 x}{1 - x} d x

limit as x approaches 0+of (5x)^{2x}

x \to 0 + lim ((5 x)^{2 x})

f (x) = x^{2} + x + 4

(\partial)/(\partial u)(2u+v)

\frac{\partial}{\partial u} (2 u + v)

Frequently Asked Questions (FAQ)

What is the derivative of 8xe^{6x} ?
The derivative of 8xe^{6x} is 8(e^{6x}+6e^{6x}x)
What is the first derivative of 8xe^{6x} ?
The first derivative of 8xe^{6x} is 8(e^{6x}+6e^{6x}x)