What is the derivative of 7xe^{6x} ?

The derivative of 7xe^{6x} is 7(e^{6x}+6e^{6x}x)

What is the first derivative of 7xe^{6x} ?

The first derivative of 7xe^{6x} is 7(e^{6x}+6e^{6x}x)

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derivative of

7 x e^{6 x}

7 (e^{6 x} + 6 e^{6 x} x)

Solution steps

\frac{d}{d x} (7 x e^{6 x})

Take the constant out:

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

= 7 \frac{d}{d x} (x e^{6 x})

Apply the Product Rule:

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

f = x, g = e^{6 x}

= 7 (\frac{d x}{d x} e^{6 x} + \frac{d}{d x} (e^{6 x}) x)

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 7 (1 \cdot e^{6 x} + e^{6 x} \cdot 6 x)

Simplify

= 7 (e^{6 x} + 6 e^{6 x} x)

What is the derivative of 7xe^{6x} ?
The derivative of 7xe^{6x} is 7(e^{6x}+6e^{6x}x)
What is the first derivative of 7xe^{6x} ?
The first derivative of 7xe^{6x} is 7(e^{6x}+6e^{6x}x)