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Popular >

derivative of (x^3+9)e^x

Solution

derivative of

(x^{3} + 9) e^{x}

Solution

3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Solution steps

\frac{d}{d x} ((x^{3} + 9) e^{x})

Apply the Product Rule:

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

f = x^{3} + 9, g = e^{x}

= \frac{d}{d x} (x^{3} + 9) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 9)

\frac{d}{d x} (x^{3} + 9) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 9)

Popular Examples

integral of (((x-2)^4))/(sqrt(4x-x^2))

\int \frac{( ( x - 2 ) ^{4} )}{4 x - x ^{2}} d x

derivative of ((-2x-3)^7)/((4x+2)^4)derivative of

\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}}

derivative of (x^3+5/(x^2+1))

\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 1})

limit as t approaches infinity of x

t \to \infty lim (x)

integral from 0 to 9 of pie^{-(2x)/9}

\int_{0}^{9} π e^{- \frac{2 x}{9}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+9)e^x ?
The derivative of (x^3+9)e^x is 3x^2e^x+e^x(x^3+9)
What is the first derivative of (x^3+9)e^x ?
The first derivative of (x^3+9)e^x is 3x^2e^x+e^x(x^3+9)