What is the derivative of x^3(1-x)^{100}+x^4-5pi ?

The derivative of x^3(1-x)^{100}+x^4-5pi is 4x^3-100x^3(-x+1)^{99}+3x^2(-x+1)^{100}

What is the first derivative of x^3(1-x)^{100}+x^4-5pi ?

The first derivative of x^3(1-x)^{100}+x^4-5pi is 4x^3-100x^3(-x+1)^{99}+3x^2(-x+1)^{100}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x^{3} (1 - x)^{100} + x^{4} - 5 π

4 x^{3} - 100 x^{3} (- x + 1)^{99} + 3 x^{2} (- x + 1)^{100}

Solution steps

\frac{d}{d x} (x^{3} (1 - x)^{100} + x^{4} - 5 π)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3} (1 - x)^{100}) + \frac{d}{d x} (x^{4}) - \frac{d}{d x} (5 π)

\frac{d}{d x} (x^{3} (1 - x)^{100}) = 3 x^{2} (1 - x)^{100} - 100 x^{3} (1 - x)^{99}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (5 π) = 0

= 3 x^{2} (1 - x)^{100} - 100 x^{3} (1 - x)^{99} + 4 x^{3} - 0

Simplify

= 4 x^{3} - 100 x^{3} (- x + 1)^{99} + 3 x^{2} (- x + 1)^{100}

\frac{d}{d x} (3 x^{3} - 64 x)

x \to 1 + lim (tan (\frac{π x}{2}))

x \to \frac{1}{2} lim (x)

\frac{d}{d x} (- x \cdot ln (x))

x \to 0 lim (\frac{2. 8 ^{x} - 1}{x})

What is the derivative of x^3(1-x)^{100}+x^4-5pi ?
The derivative of x^3(1-x)^{100}+x^4-5pi is 4x^3-100x^3(-x+1)^{99}+3x^2(-x+1)^{100}
What is the first derivative of x^3(1-x)^{100}+x^4-5pi ?
The first derivative of x^3(1-x)^{100}+x^4-5pi is 4x^3-100x^3(-x+1)^{99}+3x^2(-x+1)^{100}