What is the derivative of (6x^2-10xe^x) ?

The derivative of (6x^2-10xe^x) is 6e^xx^2+2e^xx-10e^x

What is the first derivative of (6x^2-10xe^x) ?

The first derivative of (6x^2-10xe^x) is 6e^xx^2+2e^xx-10e^x

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\frac{d}{d x} ((6 x^{2} - 10 x) e^{x})

6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

Solution steps

\frac{d}{d x} ((6 x^{2} - 10 x) e^{x})

Apply the Product Rule:

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

f = 6 x^{2} - 10 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 10 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 10 x)

\frac{d}{d x} (6 x^{2} - 10 x) = 12 x - 10

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

= (12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x)

Simplify

(12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x) : 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

= 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

n = 1 \sum \infty e^{(2 n - 1)}

\int - 40 t^{\frac{2}{3}} d t

y = 7 e^{x} x

y = x^{3} + 1, y = 4 x + 1

\int \frac{1}{( x ^{2} - 25 ) ^{\frac{3}{2}}} d x

What is the derivative of (6x^2-10xe^x) ?
The derivative of (6x^2-10xe^x) is 6e^xx^2+2e^xx-10e^x
What is the first derivative of (6x^2-10xe^x) ?
The first derivative of (6x^2-10xe^x) is 6e^xx^2+2e^xx-10e^x