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Popular >

derivative of (2x^3-7/(x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x^{3} - 7) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}}

Simplify

\frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{3} + 7 )}{x ^{3}}

= \frac{2 ( x ^{3} + 7 )}{x ^{3}}

Graph

Popular Examples

(dy)/(dx)=100-y

\frac{d y}{d x} = 100 - y

limit as x approaches infinity of (1+1/(2x+1))^{sqrt(x^{2-3)}}

x \to \infty lim ((1 + \frac{1}{2 x + 1})^{x^{2 - 3}})

integral from 0 to 1 of (x^2-3x+6)

\int_{0}^{1} (x^{2} - 3 x + 6) d x

limit as x approaches 0 of+(xsin(1/x))

x \to 0 lim (+ (x sin (\frac{1}{x})))

y^{'''}+y^{''}=3e^x+4x^2

y^{^{'''}} + y^{^{''}} = 3 e^{x} + 4 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (2x^3-7/(x^2)) ?
The derivative of (2x^3-7/(x^2)) is (2(x^3+7))/(x^3)
What is the first derivative of (2x^3-7/(x^2)) ?
The first derivative of (2x^3-7/(x^2)) is (2(x^3+7))/(x^3)