What is the derivative of e^x(9-5x+5x^2) ?

The derivative of e^x(9-5x+5x^2) is 5e^xx^2+5e^xx+4e^x

What is the first derivative of e^x(9-5x+5x^2) ?

The first derivative of e^x(9-5x+5x^2) is 5e^xx^2+5e^xx+4e^x

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derivative of

e^{x} (9 - 5 x + 5 x^{2})

5 e^{x} x^{2} + 5 e^{x} x + 4 e^{x}

Solution steps

\frac{d}{d x} (e^{x} (9 - 5 x + 5 x^{2}))

Apply the Product Rule:

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

f = e^{x}, g = 9 - 5 x + 5 x^{2}

= \frac{d}{d x} (e^{x}) (9 - 5 x + 5 x^{2}) + \frac{d}{d x} (9 - 5 x + 5 x^{2}) e^{x}

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

\frac{d}{d x} (9 - 5 x + 5 x^{2}) = 10 x - 5

= e^{x} (9 - 5 x + 5 x^{2}) + (10 x - 5) e^{x}

Simplify

e^{x} (9 - 5 x + 5 x^{2}) + (10 x - 5) e^{x} : 5 e^{x} x^{2} + 5 e^{x} x + 4 e^{x}

= 5 e^{x} x^{2} + 5 e^{x} x + 4 e^{x}

\frac{d}{d x} (cos (- \frac{x}{3}))

t^{2} sin (3 t)

\int_{- 3}^{3} 12 - x^{2} - (x^{2} - 6) d x

x \to 2 lim (9 + (- 12))

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

What is the derivative of e^x(9-5x+5x^2) ?
The derivative of e^x(9-5x+5x^2) is 5e^xx^2+5e^xx+4e^x
What is the first derivative of e^x(9-5x+5x^2) ?
The first derivative of e^x(9-5x+5x^2) is 5e^xx^2+5e^xx+4e^x