What is the derivative of A(e^{9x}+9e^{9x}x) ?

The derivative of A(e^{9x}+9e^{9x}x) is A(81e^{9x}x+18e^{9x})

What is the first derivative of A(e^{9x}+9e^{9x}x) ?

The first derivative of A(e^{9x}+9e^{9x}x) is A(81e^{9x}x+18e^{9x})

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

A (81 e^{9 x} x + 18 e^{9 x})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Expand

e^{9 x} \cdot 9 + 9 (9 e^{9 x} x + e^{9 x}) : 81 e^{9 x} x + 18 e^{9 x}

= A (81 e^{9 x} x + 18 e^{9 x})

What is the derivative of A(e^{9x}+9e^{9x}x) ?
The derivative of A(e^{9x}+9e^{9x}x) is A(81e^{9x}x+18e^{9x})
What is the first derivative of A(e^{9x}+9e^{9x}x) ?
The first derivative of A(e^{9x}+9e^{9x}x) is A(81e^{9x}x+18e^{9x})