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Popular >

derivative of (7x^2-1/x)

Solution

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

Solution

\frac{7 x ^{2} + 1}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (7 x^{2} - 1) = 14 x

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

= \frac{14 xx - 1 \cdot ( 7 x ^{2} - 1 )}{x ^{2}}

Simplify

\frac{14 xx - 1 \cdot ( 7 x ^{2} - 1 )}{x ^{2}} : \frac{7 x ^{2} + 1}{x ^{2}}

= \frac{7 x ^{2} + 1}{x ^{2}}

Graph

Popular Examples

y^{''}+4y=0,y(0)=1,y^'(0)=4

y^{^{''}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 4

(dy)/(dx)=32x^3y^3,y(0)=k

\frac{d y}{d x} = 32 x^{3} y^{3}, y (0) = k

integral of [(a^3)/(x^2+a^2)]^2

\int [\frac{a ^{3}}{x ^{2} + a ^{2}}]^{2} d x

limit as x approaches 4 of 3x+5

x \to 4 lim (3 x + 5)

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

n = 1 \sum \infty (\frac{n}{n + 4})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of (7x^2-1/x) ?
The derivative of (7x^2-1/x) is (7x^2+1)/(x^2)
What is the first derivative of (7x^2-1/x) ?
The first derivative of (7x^2-1/x) is (7x^2+1)/(x^2)