en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^5(x^6+1)

Solution

\frac{d}{d x} (x^{5} (x^{6} + 1))

Solution

11 x^{10} + 5 x^{4}

Solution steps

\frac{d}{d x} (x^{5} (x^{6} + 1))

Apply the Product Rule:

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

f = x^{5}, g = x^{6} + 1

= \frac{d}{d x} (x^{5}) (x^{6} + 1) + \frac{d}{d x} (x^{6} + 1) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (x^{6} + 1) = 6 x^{5}

= 5 x^{4} (x^{6} + 1) + 6 x^{5} x^{5}

Simplify

5 x^{4} (x^{6} + 1) + 6 x^{5} x^{5} : 11 x^{10} + 5 x^{4}

= 11 x^{10} + 5 x^{4}

Popular Examples

integral of (3x^2-1)/(x^3-x+5)

\int \frac{3 x ^{2} - 1}{x ^{3} - x + 5} d x

tangent of 7-x-x^2 tangent of

7 - x - x^{2}

limit as x approaches 3-of x/(x^2-9)

x \to 3 - lim (\frac{x}{x ^{2} - 9})

(\partial)/(\partial x)(β(x)^{-γ})

\frac{\partial}{\partial x} (β (x)^{- γ})

integral from ln(3) to ln(7) of e^x

\int_{l n (3)}^{l n (7)} e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^5(x^6+1) ?
The derivative of x^5(x^6+1) is 11x^{10}+5x^4
What is the first derivative of x^5(x^6+1) ?
The first derivative of x^5(x^6+1) is 11x^{10}+5x^4