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Popular >

derivative of 8xe^{4x}

Solution

\frac{d}{d x} (8 x e^{4 x})

Solution

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

Solution steps

\frac{d}{d x} (8 x e^{4 x})

Take the constant out:

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

= 8 \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}

= 8 (\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

= 8 (1 \cdot e^{4 x} + e^{4 x} \cdot 4 x)

Simplify

= 8 (e^{4 x} + 4 e^{4 x} x)

Popular Examples

integral of (sin^2(x))/(x^2)

\int \frac{sin ^{2} ( x )}{x ^{2}} d x

derivative of f(x)=(e^x)/(1-e^x)derivative of

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

15y^{''}-7y^'-4y=0

15 y^{^{''}} - 7 y^{^{'}} - 4 y = 0

limit as t approaches 0 of tan(4t)

t \to 0 lim (tan (4 t))

integral of 2t-3sin(t)

\int 2 t - 3 sin (t) d t

Frequently Asked Questions (FAQ)

What is the derivative of 8xe^{4x} ?
The derivative of 8xe^{4x} is 8(e^{4x}+4e^{4x}x)
What is the first derivative of 8xe^{4x} ?
The first derivative of 8xe^{4x} is 8(e^{4x}+4e^{4x}x)