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Popular >

derivative of (8x^3-9/(x^2))

Solution

\frac{d}{d x} (\frac{8 x ^{3} - 9}{x ^{2}})

Solution

\frac{2 ( 4 x ^{3} + 9 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{8 x ^{3} - 9}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{3} - 9 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 8 x ^{3} - 9 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (8 x^{3} - 9) = 24 x^{2}

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

= \frac{24 x ^{2} x ^{2} - 2 x ( 8 x ^{3} - 9 )}{( x ^{2} ) ^{2}}

Simplify

\frac{24 x ^{2} x ^{2} - 2 x ( 8 x ^{3} - 9 )}{( x ^{2} ) ^{2}} : \frac{2 ( 4 x ^{3} + 9 )}{x ^{3}}

= \frac{2 ( 4 x ^{3} + 9 )}{x ^{3}}

Graph

Popular Examples

integral of 1/(u^5)

\int \frac{1}{u ^{5}} d u

derivative of 4cos(x-sin(x))

\frac{d}{d x} (4 cos (x) - sin (x))

x^2y^{''}-3xy^'+3y=0,y(1)=5,y^'(1)=3

x^{2} y^{^{''}} - 3 x y^{^{'}} + 3 y = 0, y (1) = 5, y^{^{'}} (1) = 3

x(e^{y/x}-1)y^'=e^{y/x}(y-x)

x (e^{\frac{y}{x}} - 1) y^{^{'}} = e^{\frac{y}{x}} (y - x)

derivative of y=ln(x^5)+e^x-ln(e^2)derivative of

y = ln (x^{5}) + e^{x} - ln (e^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (8x^3-9/(x^2)) ?
The derivative of (8x^3-9/(x^2)) is (2(4x^3+9))/(x^3)
What is the first derivative of (8x^3-9/(x^2)) ?
The first derivative of (8x^3-9/(x^2)) is (2(4x^3+9))/(x^3)