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Popular >

derivative of 1/(1+x^4)

Solution

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

Solution

- \frac{4 x ^{3}}{( 1 + x ^{4} ) ^{2}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + x^{4}) = 4 x^{3}

= - \frac{1}{( 1 + x ^{4} ) ^{2}} \cdot 4 x^{3}

Simplify

- \frac{1}{( 1 + x ^{4} ) ^{2}} \cdot 4 x^{3} : - \frac{4 x ^{3}}{( 1 + x ^{4} ) ^{2}}

= - \frac{4 x ^{3}}{( 1 + x ^{4} ) ^{2}}

Popular Examples

derivative of 4sec(x-8cos(x))

\frac{d}{d x} (4 sec (x) - 8 cos (x))

area y=x^3,y=x,x>= 0 area

y = x^{3}, y = x, x \geq 0

integral from 0 to 1 of x^9e^{x^5}

\int_{0}^{1} x^{9} e^{x^{5}} d x

limit as x approaches 0 of ((ln(cos(2x))))/(x^2)

x \to 0 lim (\frac{( ln ( cos ( 2 x ) ) )}{x ^{2}})

x^2y^{''}+9xy^'-20y= 5/(x^3)

x^{2} y^{^{''}} + 9 x y^{^{'}} - 20 y = \frac{5}{x ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of 1/(1+x^4) ?
The derivative of 1/(1+x^4) is -(4x^3)/((1+x^4)^2)
What is the first derivative of 1/(1+x^4) ?
The first derivative of 1/(1+x^4) is -(4x^3)/((1+x^4)^2)