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Popular >

derivative of 5xe^{4x}

Solution

\frac{d}{d x} (5 x e^{4 x})

Solution

5 (e^{4 x} + 4 e^{4 x} x)

Solution steps

\frac{d}{d x} (5 x e^{4 x})

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{4 x})

Apply the Product Rule:

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

f = x, g = e^{4 x}

= 5 (\frac{d x}{d x} e^{4 x} + \frac{d}{d x} (e^{4 x}) x)

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 5 (1 \cdot e^{4 x} + e^{4 x} \cdot 4 x)

Simplify

= 5 (e^{4 x} + 4 e^{4 x} x)

Popular Examples

(\partial)/(\partial x)((63)/((9+x^2+y^2)))

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

(\partial)/(\partial z)(1/(x^2yz))

\frac{\partial}{\partial z} (\frac{1}{x ^{2} yz})

integral of sqrt(9+4x^2)

\int 9 + 4 x^{2} d x

inverse oflaplace ((s+2))/(s^2+s+1)-1/s inverse laplace

\frac{( s + 2 )}{s ^{2} + s + 1} - \frac{1}{s}

derivative of 5.2x+2.3 derivative of

5.2 x + 2.3

Frequently Asked Questions (FAQ)

What is the derivative of 5xe^{4x} ?
The derivative of 5xe^{4x} is 5(e^{4x}+4e^{4x}x)
What is the first derivative of 5xe^{4x} ?
The first derivative of 5xe^{4x} is 5(e^{4x}+4e^{4x}x)