What is the derivative of (2x^3-x^2+5x/(x^2-25)) ?

The derivative of (2x^3-x^2+5x/(x^2-25)) is (2x^4-155x^2+50x-125)/((x^2-25)^2)

What is the first derivative of (2x^3-x^2+5x/(x^2-25)) ?

The first derivative of (2x^3-x^2+5x/(x^2-25)) is (2x^4-155x^2+50x-125)/((x^2-25)^2)

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\frac{d}{d x} (\frac{2 x ^{3} - x ^{2} + 5 x}{x ^{2} - 25})

\frac{2 x ^{4} - 155 x ^{2} + 50 x - 125}{( x ^{2} - 25 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{3} - x ^{2} + 5 x}{x ^{2} - 25})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} - x ^{2} + 5 x ) ( x ^{2} - 25 ) - \frac{d}{d x} ( x ^{2} - 25 ) ( 2 x ^{3} - x ^{2} + 5 x )}{( x ^{2} - 25 ) ^{2}}

\frac{d}{d x} (2 x^{3} - x^{2} + 5 x) = 6 x^{2} - 2 x + 5

\frac{d}{d x} (x^{2} - 25) = 2 x

= \frac{( 6 x ^{2} - 2 x + 5 ) ( x ^{2} - 25 ) - 2 x ( 2 x ^{3} - x ^{2} + 5 x )}{( x ^{2} - 25 ) ^{2}}

Expand

(6 x^{2} - 2 x + 5) (x^{2} - 25) - 2 x (2 x^{3} - x^{2} + 5 x) : 2 x^{4} - 155 x^{2} + 50 x - 125

= \frac{2 x ^{4} - 155 x ^{2} + 50 x - 125}{( x ^{2} - 25 ) ^{2}}

\int \frac{6 - y}{y - 1} d y

\int_{2}^{8} (10 - x) d x

f (x) = (2 x^{7} - 3 x^{5} + 2)^{22}

\frac{s + 3}{s ^{2} + 3 s + 2}

\frac{\partial}{\partial x} (x y - z)

What is the derivative of (2x^3-x^2+5x/(x^2-25)) ?
The derivative of (2x^3-x^2+5x/(x^2-25)) is (2x^4-155x^2+50x-125)/((x^2-25)^2)
What is the first derivative of (2x^3-x^2+5x/(x^2-25)) ?
The first derivative of (2x^3-x^2+5x/(x^2-25)) is (2x^4-155x^2+50x-125)/((x^2-25)^2)