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Popular >

derivative of 4xe^{3x}

Solution

\frac{d}{d x} (4 x e^{3 x})

Solution

4 (e^{3 x} + 3 e^{3 x} x)

Solution steps

\frac{d}{d x} (4 x e^{3 x})

Take the constant out:

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

= 4 \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}

= 4 (\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

= 4 (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

Simplify

= 4 (e^{3 x} + 3 e^{3 x} x)

Popular Examples

derivative of x/(sin(x+cos(x)))

\frac{d}{d x} (\frac{x}{sin ( x ) + cos ( x )})

derivative of e^{5x}cos(3x)

\frac{d}{d x} (e^{5 x} cos (3 x))

derivative of (x^4/(3-x^3))

\frac{d}{d x} (\frac{x ^{4}}{3 - x ^{3}})

integral from 0 to pi/3 of 1sec^2(x)

\int_{0}^{\frac{π}{3}} 1 sec^{2} (x) d x

integral of 5/(xln(4x))

\int \frac{5}{x ln ( 4 x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of 4xe^{3x} ?
The derivative of 4xe^{3x} is 4(e^{3x}+3e^{3x}x)
What is the first derivative of 4xe^{3x} ?
The first derivative of 4xe^{3x} is 4(e^{3x}+3e^{3x}x)