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Popular >

derivative of (4x^2+1^{-50})

Solution

\frac{d}{d x} ((4 x^{2} + 1)^{- 50})

Solution

- \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

Solution steps

\frac{d}{d x} ((4 x^{2} + 1)^{- 50})

Apply the chain rule:

- \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \frac{d}{d x} (4 x^{2} + 1)

= - \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \frac{d}{d x} (4 x^{2} + 1)

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= - \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \cdot 8 x

Simplify

- \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \cdot 8 x : - \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

= - \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

Graph

Popular Examples

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

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\int 2 + x^{2} d x

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\frac{d}{d x} (\frac{y}{3 x})

(dy)/(dx)=-2y,y(0)=3

\frac{d y}{d x} = - 2 y, y (0) = 3

derivative of (3x^2+ln(x)*(5x^3)^x)

\frac{d}{d x} ((3 x^{2} + ln (x)) \cdot (5 x^{3})^{x})

Frequently Asked Questions (FAQ)

What is the derivative of (4x^2+1^{-50}) ?
The derivative of (4x^2+1^{-50}) is -(400x)/((4x^2+1)^{51)}
What is the first derivative of (4x^2+1^{-50}) ?
The first derivative of (4x^2+1^{-50}) is -(400x)/((4x^2+1)^{51)}