en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=5x^2e^{2x}

Solution

derivative of

y = 5 x^{2} e^{2 x}

Solution

5 (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = e^{2 x}

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

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

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

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

Popular Examples

derivative of y=4*5^x derivative of

y = 4 \cdot 5^{x}

derivative of (x(x^2-1)/(sqrt(x^2+1)))

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

limit as x approaches 0 of x^2(sin(1/x))

x \to 0 lim (x^{2} (sin (\frac{1}{x})))

integral of x^2sqrt(3+2x-x^2)

\int x^{2} 3 + 2 x - x^{2} d x

derivative of 4e^{x/2}-3e^{-x}

\frac{d}{d x} (4 e^{\frac{x}{2}} - 3 e^{- x})

Frequently Asked Questions (FAQ)

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