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Popular >

derivative of (x^2+16/x)

Solution

\frac{d}{d x} (\frac{x ^{2} + 16}{x})

Solution

\frac{x ^{2} - 16}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 16}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 16 ) x - \frac{d x}{d x} ( x ^{2} + 16 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 16) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 16 )}{x ^{2}}

Simplify

\frac{2 xx - 1 \cdot ( x ^{2} + 16 )}{x ^{2}} : \frac{x ^{2} - 16}{x ^{2}}

= \frac{x ^{2} - 16}{x ^{2}}

Popular Examples

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

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

derivative of f(x)=(40x^5)/(e^x)derivative of

f (x) = \frac{40 x ^{5}}{e ^{x}}

integral of (e^x)/(5+e^x)

\int \frac{e ^{x}}{5 + e ^{x}} d x

sum from n=1 to infinity of (n^5)/(4^n)

n = 1 \sum \infty \frac{n ^{5}}{4 ^{n}}

integral from 2 to infinity of 0

\int_{2}^{\infty} 0 d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+16/x) ?
The derivative of (x^2+16/x) is (x^2-16)/(x^2)
What is the first derivative of (x^2+16/x) ?
The first derivative of (x^2+16/x) is (x^2-16)/(x^2)