en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=xe^{9x}

Solution

derivative of

y = x e^{9 x}

Solution

e^{9 x} + 9 e^{9 x} x

Solution steps

\frac{d}{d x} (x e^{9 x})

Apply the Product Rule:

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

f = x, g = e^{9 x}

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

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

\frac{d}{d x} (e^{9 x}) = e^{9 x} \cdot 9

= 1 \cdot e^{9 x} + e^{9 x} \cdot 9 x

Simplify

= e^{9 x} + 9 e^{9 x} x

Popular Examples

derivative of 1/3 (x^2-2)^{3/2}derivative of

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

integral of ((x^2-x+36))/(x^3+6x)

\int \frac{( x ^{2} - x + 36 )}{x ^{3} + 6 x} d x

tangent of y=2sin(x),(pi/6 ,1)tangent of

y = 2 sin (x), (\frac{π}{6}, 1)

limit as x approaches 2+of (x^2)/(x^2-4)

x \to 2 + lim (\frac{x ^{2}}{x ^{2} - 4})

derivative of 1-(1-0.01x)^3 derivative of

1 - (1 - 0.01 x)^{3}

Frequently Asked Questions (FAQ)

What is the derivative of y=xe^{9x} ?
The derivative of y=xe^{9x} is e^{9x}+9e^{9x}x
What is the first derivative of y=xe^{9x} ?
The first derivative of y=xe^{9x} is e^{9x}+9e^{9x}x