en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (6x^2-9x)e^x

Solution

derivative of

(6 x^{2} - 9 x) e^{x}

Solution

6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

Solution steps

\frac{d}{d x} ((6 x^{2} - 9 x) e^{x})

Apply the Product Rule:

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

f = 6 x^{2} - 9 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 9 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 9 x)

\frac{d}{d x} (6 x^{2} - 9 x) = 12 x - 9

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

= (12 x - 9) e^{x} + e^{x} (6 x^{2} - 9 x)

Simplify

(12 x - 9) e^{x} + e^{x} (6 x^{2} - 9 x) : 6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

= 6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

Popular Examples

integral of (t^3)/m-(cos(t))/m

\int \frac{t ^{3}}{m} - \frac{cos ( t )}{m} d t

(\partial)/(\partial x)(y^2ln(y)-2xy^2)

\frac{\partial}{\partial x} (y^{2} ln (y) - 2 x y^{2})

derivative of (x^2-9x+20/((x+2)(x-2)))

\frac{d}{d x} (\frac{x ^{2} - 9 x + 20}{( x + 2 ) ( x - 2 )})

derivative of (log_{10}(x)^{sinh(x)})

\frac{d}{d x} ((lo g_{10} (x))^{s i n h (x)})

tangent of f(x)=x^2-4,\at a=1 tangent of

f (x) = x^{2} - 4, at a = 1

Frequently Asked Questions (FAQ)

What is the derivative of (6x^2-9x)e^x ?
The derivative of (6x^2-9x)e^x is 6e^xx^2+3e^xx-9e^x
What is the first derivative of (6x^2-9x)e^x ?
The first derivative of (6x^2-9x)e^x is 6e^xx^2+3e^xx-9e^x