What is the derivative of e^x(x+6) ?

The derivative of e^x(x+6) is e^xx+7e^x

What is the first derivative of e^x(x+6) ?

The first derivative of e^x(x+6) is e^xx+7e^x

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

e^{x} x + 7 e^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (x + 6) = 1

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

Simplify

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

= e^{x} x + 7 e^{x}

x \to - 9 lim (\frac{9 - ∣ x ∣}{9 + x})

\int e^{- x} sin (w x) d x

\frac{d}{d x} (x^{2} y + y^{2})

\int (2 x + 1) (2 x^{2} + 2 x)^{\frac{3}{4}} d x

\frac{\partial}{\partial x} (5 z^{2} cot (x z))

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