What is the derivative of f(x)=(3x+7)e^x ?

The derivative of f(x)=(3x+7)e^x is 3e^xx+10e^x

What is the first derivative of f(x)=(3x+7)e^x ?

The first derivative of f(x)=(3x+7)e^x is 3e^xx+10e^x

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derivative of

f (x) = (3 x + 7) e^{x}

3 e^{x} x + 10 e^{x}

Solution steps

\frac{d}{d x} ((3 x + 7) e^{x})

Apply the Product Rule:

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

f = 3 x + 7, g = e^{x}

= \frac{d}{d x} (3 x + 7) e^{x} + \frac{d}{d x} (e^{x}) (3 x + 7)

\frac{d}{d x} (3 x + 7) = 3

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

= 3 e^{x} + e^{x} (3 x + 7)

Simplify

3 e^{x} + e^{x} (3 x + 7) : 3 e^{x} x + 10 e^{x}

= 3 e^{x} x + 10 e^{x}

x^{2} + 10

\frac{d}{d x} (1.394 (1.006)^{x})

\int \frac{1}{( x ^{2} - 196 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (arccot (4 x))

\frac{d}{d x} (y^{2} (2 - x) - x^{3})

What is the derivative of f(x)=(3x+7)e^x ?
The derivative of f(x)=(3x+7)e^x is 3e^xx+10e^x
What is the first derivative of f(x)=(3x+7)e^x ?
The first derivative of f(x)=(3x+7)e^x is 3e^xx+10e^x