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Popular >

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

Solution

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

Solution

3 x^{2} e^{3 x} + e^{3 x} \cdot 3 (x^{3} + 4)

Solution steps

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

Apply the Product Rule:

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

f = x^{3} + 4, g = e^{3 x}

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

\frac{d}{d x} (x^{3} + 4) = 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} + 4)

Popular Examples

integral of e^{x+y^2-z}

\int e^{x + y^{2} - z} d x

integral of (ln(-2x))/(5x)

\int \frac{ln ( - 2 x )}{5 x} d x

limit as t approaches 0 of (e^t-1)/(t^9)

t \to 0 lim (\frac{e ^{t} - 1}{t ^{9}})

area y=x^2-7,y=6x area

y = x^{2} - 7, y = 6 x

6y^{'''}+4y^{''}=0

6 y^{^{'''}} + 4 y^{^{''}} = 0

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+4e^{3x}) ?
The derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)
What is the first derivative of (x^3+4e^{3x}) ?
The first derivative of (x^3+4e^{3x}) is 3x^2e^{3x}+e^{3x}*3(x^3+4)