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

The derivative of y=(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 y=(x^2-2x+2)e^{(5x)/2} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (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}}

\int sec (θ) tan (θ) d θ

\frac{d}{d t} (p (t) e^{t})

y = 5 + 1 - x, (- 8, 8)

\int_{0}^{12} 2 π y (144 - y^{2}) d y

\int cos (x) sec (x) sin (x) d x

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