What is the derivative of (x-3e^x) ?

The derivative of (x-3e^x) is e^xx-2e^x

What is the first derivative of (x-3e^x) ?

The first derivative of (x-3e^x) is e^xx-2e^x

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\frac{d}{d x} ((x - 3) e^{x})

e^{x} x - 2 e^{x}

Solution steps

\frac{d}{d x} ((x - 3) e^{x})

Apply the Product Rule:

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

f = x - 3, g = e^{x}

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

\frac{d}{d x} (x - 3) = 1

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

= 1 \cdot e^{x} + e^{x} (x - 3)

Simplify

1 \cdot e^{x} + e^{x} (x - 3) : e^{x} x - 2 e^{x}

= e^{x} x - 2 e^{x}

x \to 0 lim (\frac{( tan ( x ) )}{x})

\int_{0}^{1} x^{2} - 1 d x

\int (3 x^{4} + x^{5}) d x

(1 + y^{2}) d x + x y d y = 0

x = \frac{7}{y}, x = \frac{y}{9}, x = 9 y

What is the derivative of (x-3e^x) ?
The derivative of (x-3e^x) is e^xx-2e^x
What is the first derivative of (x-3e^x) ?
The first derivative of (x-3e^x) is e^xx-2e^x