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Popular >

derivative of f(x)=(x)^{(3)}e^{(3x)}

Solution

derivative of

f (x) = (x)^{(3)} e^{(3 x)}

Solution

3 x^{2} e^{3 x} + e^{3 x} \cdot 3 x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = e^{3 x}

= \frac{d}{d x} (x^{3}) e^{3 x} + \frac{d}{d x} (e^{3 x}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 3 x^{2} e^{3 x} + e^{3 x} \cdot 3 x^{3}

Popular Examples

limit as x approaches 2+of e^{(1+x)/(2-x)}

x \to 2 + lim (e^{\frac{1 + x}{2 - x}})

y^'+6y=2t+3,y(0)=1

y^{^{'}} + 6 y = 2 t + 3, y (0) = 1

integral of (5x+1)/(x^2-1)

\int \frac{5 x + 1}{x ^{2} - 1} d x

limit as x approaches 5-of x/(x-5)

x \to 5 - lim (\frac{x}{x - 5})

y^{^{''}} - 2 y^{^{'}} = 6

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x)^{(3)}e^{(3x)} ?
The derivative of f(x)=(x)^{(3)}e^{(3x)} is 3x^2e^{3x}+e^{3x}*3x^3
What is the first derivative of f(x)=(x)^{(3)}e^{(3x)} ?
The first derivative of f(x)=(x)^{(3)}e^{(3x)} is 3x^2e^{3x}+e^{3x}*3x^3