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Popular >

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

Solution

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

Solution

\frac{- 4 x - 5}{x ^{6}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x + 1 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( x + 1 )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (x + 1) = 1

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

= \frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}}

Simplify

\frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}} : \frac{- 4 x - 5}{x ^{6}}

= \frac{- 4 x - 5}{x ^{6}}

Popular Examples

(\partial)/(\partial y)(4x^2y-5xy^2)

\frac{\partial}{\partial y} (4 x^{2} y - 5 x y^{2})

area y=9-0.25x^2,y=0,[2,5]area

y = 9 - 0.25 x^{2}, y = 0, [2, 5]

derivative of 1/(3x+1)derivative of

\frac{1}{3 x + 1}

derivative of (2x^2-1^2(7x+1)^3)

\frac{d}{d x} ((2 x^{2} - 1)^{2} (7 x + 1)^{3})

derivative of f(x)=((x^2))/(x^2+9)derivative of

f (x) = \frac{( x ^{2} )}{x ^{2} + 9}

Frequently Asked Questions (FAQ)

What is the derivative of (x+1/(x^5)) ?
The derivative of (x+1/(x^5)) is (-4x-5)/(x^6)
What is the first derivative of (x+1/(x^5)) ?
The first derivative of (x+1/(x^5)) is (-4x-5)/(x^6)