en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 7x^3e^x

Solution

derivative of

7 x^{3} e^{x}

Solution

7 (3 x^{2} e^{x} + e^{x} x^{3})

Solution steps

\frac{d}{d x} (7 x^{3} e^{x})

Take the constant out:

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

= 7 \frac{d}{d x} (x^{3} e^{x})

Apply the Product Rule:

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

f = x^{3}, g = e^{x}

= 7 (\frac{d}{d x} (x^{3}) e^{x} + \frac{d}{d x} (e^{x}) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 7 (3 x^{2} e^{x} + e^{x} x^{3})

Popular Examples

tangent of f(x)=-1/((x-5)^2),\at x=-4 tangent of

f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 4

integral of (x^3+3x-1)/(x^4-4x^2)

\int \frac{x ^{3} + 3 x - 1}{x ^{4} - 4 x ^{2}} d x

limit as x approaches 0-of (e^{3x})/(2x)

x \to 0 - lim (\frac{e ^{3 x}}{2 x})

(dy)/(dx)=xy^4-y

\frac{d y}{d x} = x y^{4} - y

limit as x approaches 1-f of x

x \to 1 - f lim (x)

Frequently Asked Questions (FAQ)

What is the derivative of 7x^3e^x ?
The derivative of 7x^3e^x is 7(3x^2e^x+e^xx^3)
What is the first derivative of 7x^3e^x ?
The first derivative of 7x^3e^x is 7(3x^2e^x+e^xx^3)