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Popular >

derivative of (x^5+1)/x

Solution

derivative of

\frac{x ^{5} + 1}{x}

Solution

\frac{4 x ^{5} - 1}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{5} + 1) = 5 x^{4}

\frac{d x}{d x} = 1

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

Simplify

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

= \frac{4 x ^{5} - 1}{x ^{2}}

Popular Examples

integral from 0 to 1 of (8y)/(e^{2y)}

\int_{0}^{1} \frac{8 y}{e ^{2 y}} d y

integral from 0 to 1 of 2pix(x^3-x^4)

\int_{0}^{1} 2 π x (x^{3} - x^{4}) d x

integral of x/((x-3)^2)

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

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

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

integral of 1/(-x^2+6x-10)

\int \frac{1}{- x ^{2} + 6 x - 10} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^5+1)/x ?
The derivative of (x^5+1)/x is (4x^5-1)/(x^2)
What is the first derivative of (x^5+1)/x ?
The first derivative of (x^5+1)/x is (4x^5-1)/(x^2)