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Popular >

derivative of Axe^{4x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= A \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}

= A (\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

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

Simplify

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

Popular Examples

derivative of 1/6 (x-1(x+5)^5+10)

\frac{d}{d x} (\frac{1}{6} (x - 1) (x + 5)^{5} + 10)

tangent of y=9x^2+9x-3 tangent of

y = 9 x^{2} + 9 x - 3

derivative of f(x)=sin(sqrt(1+cos(x)))derivative of

f (x) = sin (1 + cos (x))

integral from 0 to 1 of (14)/(4y-1)

\int_{0}^{1} \frac{14}{4 y - 1} d y

\frac{d}{d p} (ln (p))

Frequently Asked Questions (FAQ)

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