What is the derivative of (x^2-2x+2)e^{(5x)/2} ?

The derivative of (x^2-2x+2)e^{(5x)/2} is (5e^{(5x)/2}x^2)/(2)-3e^{(5x)/2}x+3e^{(5x)/2}

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

The first derivative of (x^2-2x+2)e^{(5x)/2} is (5e^{(5x)/2}x^2)/(2)-3e^{(5x)/2}x+3e^{(5x)/2}

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derivative of

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

\frac{5 e ^{\frac{5 x}{2}} x ^{2}}{2} - 3 e^{\frac{5 x}{2}} x + 3 e^{\frac{5 x}{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 x - 2) e^{\frac{5 x}{2}} + e^{\frac{5 x}{2}} \frac{5}{2} (x^{2} - 2 x + 2) : \frac{5 e ^{\frac{5 x}{2}} x ^{2}}{2} - 3 e^{\frac{5 x}{2}} x + 3 e^{\frac{5 x}{2}}

= \frac{5 e ^{\frac{5 x}{2}} x ^{2}}{2} - 3 e^{\frac{5 x}{2}} x + 3 e^{\frac{5 x}{2}}

x^{2} + y^{2} = 26

\frac{d}{d x} (- x^{3} + 5 x^{2} - 8 x)

\int_{0}^{2} x^{3} 7 - x^{2} d x

\frac{d}{d x} (1 - e^{- 0.1 x})

\frac{\partial}{\partial x} (x y - \frac{1}{x} - \frac{1}{y})

What is the derivative of (x^2-2x+2)e^{(5x)/2} ?
The derivative of (x^2-2x+2)e^{(5x)/2} is (5e^{(5x)/2}x^2)/(2)-3e^{(5x)/2}x+3e^{(5x)/2}
What is the first derivative of (x^2-2x+2)e^{(5x)/2} ?
The first derivative of (x^2-2x+2)e^{(5x)/2} is (5e^{(5x)/2}x^2)/(2)-3e^{(5x)/2}x+3e^{(5x)/2}