What is the derivative of 9xe^x ?

The derivative of 9xe^x is 9(e^x+e^xx)

What is the first derivative of 9xe^x ?

The first derivative of 9xe^x is 9(e^x+e^xx)

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derivative of

9 x e^{x}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

\frac{d x}{d x} = 1

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

= 9 (1 \cdot e^{x} + e^{x} x)

Simplify

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

x \to 0 lim (\frac{sin ( 2 )}{2})

\frac{d}{d x} (\frac{6 x}{( x ^{2} + 3 ) ^{2}})

- \frac{1}{2} x^{2} - 2 x + 3

x \to \infty lim (x^{3} + 1)

\frac{d}{d x} (\frac{1}{x} - \frac{4}{x ^{3}})

What is the derivative of 9xe^x ?
The derivative of 9xe^x is 9(e^x+e^xx)
What is the first derivative of 9xe^x ?
The first derivative of 9xe^x is 9(e^x+e^xx)