What is the derivative of (x^2-x+1)e^3x ?

The derivative of (x^2-x+1)e^3x is e^3(3x^2-2x+1)

What is the first derivative of (x^2-x+1)e^3x ?

The first derivative of (x^2-x+1)e^3x is e^3(3x^2-2x+1)

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derivative of

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

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

Solution steps

\frac{d}{d x} ((x^{2} - x + 1) e^{3} x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{3} \frac{d}{d x} ((x^{2} - x + 1) x)

Apply the Product Rule:

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

f = x^{2} - x + 1, g = x

= e^{3} (\frac{d}{d x} (x^{2} - x + 1) x + \frac{d x}{d x} (x^{2} - x + 1))

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

\frac{d x}{d x} = 1

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

Simplify

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

= e^{3} (3 x^{2} - 2 x + 1)

y = 6 x^{2} - 3 x^{3}

y = (5 x - 3) (\frac{4 x - 3}{x})

\frac{- 5}{( 4 x - 2 y + 2 )}

y = 5 x^{8} - 6 x + 12

f (t) = 3 + 8 t - t^{2}

What is the derivative of (x^2-x+1)e^3x ?
The derivative of (x^2-x+1)e^3x is e^3(3x^2-2x+1)
What is the first derivative of (x^2-x+1)e^3x ?
The first derivative of (x^2-x+1)e^3x is e^3(3x^2-2x+1)