What is the derivative of (x^2+5xe^x) ?

The derivative of (x^2+5xe^x) is e^xx^2+7e^xx+5e^x

What is the first derivative of (x^2+5xe^x) ?

The first derivative of (x^2+5xe^x) is e^xx^2+7e^xx+5e^x

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\frac{d}{d x} ((x^{2} + 5 x) e^{x})

e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

Solution steps

\frac{d}{d x} ((x^{2} + 5 x) e^{x})

Apply the Product Rule:

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

f = x^{2} + 5 x, g = e^{x}

= \frac{d}{d x} (x^{2} + 5 x) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} + 5 x)

\frac{d}{d x} (x^{2} + 5 x) = 2 x + 5

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

= (2 x + 5) e^{x} + e^{x} (x^{2} + 5 x)

Simplify

(2 x + 5) e^{x} + e^{x} (x^{2} + 5 x) : e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

= e^{x} x^{2} + 7 e^{x} x + 5 e^{x}

\int x^{2} y d y

\int 4 tan (t) d t

\int \frac{4 x}{1 - x ^{4}} d x

\frac{d}{d x} (5 sin (x) + x^{2})

\frac{d}{d t} (740 (1.714)^{t})

What is the derivative of (x^2+5xe^x) ?
The derivative of (x^2+5xe^x) is e^xx^2+7e^xx+5e^x
What is the first derivative of (x^2+5xe^x) ?
The first derivative of (x^2+5xe^x) is e^xx^2+7e^xx+5e^x