What is the derivative of (5x^2-x+1/(x^3+4x^2)) ?

The derivative of (5x^2-x+1/(x^3+4x^2)) is -(5x^3-2x^2-x+8)/(x^3(x+4)^2)

What is the first derivative of (5x^2-x+1/(x^3+4x^2)) ?

The first derivative of (5x^2-x+1/(x^3+4x^2)) is -(5x^3-2x^2-x+8)/(x^3(x+4)^2)

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\frac{d}{d x} (\frac{5 x ^{2} - x + 1}{x ^{3} + 4 x ^{2}})

- \frac{5 x ^{3} - 2 x ^{2} - x + 8}{x ^{3} ( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} - x + 1}{x ^{3} + 4 x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} - x + 1 ) ( x ^{3} + 4 x ^{2} ) - \frac{d}{d x} ( x ^{3} + 4 x ^{2} ) ( 5 x ^{2} - x + 1 )}{( x ^{3} + 4 x ^{2} ) ^{2}}

\frac{d}{d x} (5 x^{2} - x + 1) = 10 x - 1

\frac{d}{d x} (x^{3} + 4 x^{2}) = 3 x^{2} + 8 x

= \frac{( 10 x - 1 ) ( x ^{3} + 4 x ^{2} ) - ( 3 x ^{2} + 8 x ) ( 5 x ^{2} - x + 1 )}{( x ^{3} + 4 x ^{2} ) ^{2}}

Simplify

\frac{( 10 x - 1 ) ( x ^{3} + 4 x ^{2} ) - ( 3 x ^{2} + 8 x ) ( 5 x ^{2} - x + 1 )}{( x ^{3} + 4 x ^{2} ) ^{2}} : - \frac{5 x ^{3} - 2 x ^{2} - x + 8}{x ^{3} ( x + 4 ) ^{2}}

= - \frac{5 x ^{3} - 2 x ^{2} - x + 8}{x ^{3} ( x + 4 ) ^{2}}

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

\frac{\partial}{\partial x} (x^{9} y^{9} + 5 x^{8} y)

y^{^{''}} - y - 4 = 0

x \to - 3 lim (F (x))

\int \frac{6}{( 2 x - 1 ) ^{2}} d x

What is the derivative of (5x^2-x+1/(x^3+4x^2)) ?
The derivative of (5x^2-x+1/(x^3+4x^2)) is -(5x^3-2x^2-x+8)/(x^3(x+4)^2)
What is the first derivative of (5x^2-x+1/(x^3+4x^2)) ?
The first derivative of (5x^2-x+1/(x^3+4x^2)) is -(5x^3-2x^2-x+8)/(x^3(x+4)^2)