What is the derivative of (250000x^2/((2x+1)^2)) ?

The derivative of (250000x^2/((2x+1)^2)) is (500000x)/((2x+1)^3)

What is the first derivative of (250000x^2/((2x+1)^2)) ?

The first derivative of (250000x^2/((2x+1)^2)) is (500000x)/((2x+1)^3)

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\frac{d}{d x} (\frac{250000 x ^{2}}{( 2 x + 1 ) ^{2}})

\frac{500000 x}{( 2 x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{250000 x ^{2}}{( 2 x + 1 ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 250000 \frac{d}{d x} (\frac{x ^{2}}{( 2 x + 1 ) ^{2}})

Apply the Quotient Rule:

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

= 250000 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 2 x + 1 ) ^{2} - \frac{d}{d x} ( ( 2 x + 1 ) ^{2} ) x ^{2}}{( ( 2 x + 1 ) ^{2} ) ^{2}}

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

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

= 250000 \cdot \frac{2 x ( 2 x + 1 ) ^{2} - 4 ( 2 x + 1 ) x ^{2}}{( ( 2 x + 1 ) ^{2} ) ^{2}}

Simplify

250000 \cdot \frac{2 x ( 2 x + 1 ) ^{2} - 4 ( 2 x + 1 ) x ^{2}}{( ( 2 x + 1 ) ^{2} ) ^{2}} : \frac{500000 x}{( 2 x + 1 ) ^{3}}

= \frac{500000 x}{( 2 x + 1 ) ^{3}}

\frac{d ^{2}}{d x ^{2}} (x^{2} e^{- x^{2}})

\int 3 + 2 x y^{2} d x

\int 5 e^{3 x + 2} d x

\int 10 tan^{3} (x) d x

\frac{d}{d x} (\frac{2 ln ( x )}{x})

What is the derivative of (250000x^2/((2x+1)^2)) ?
The derivative of (250000x^2/((2x+1)^2)) is (500000x)/((2x+1)^3)
What is the first derivative of (250000x^2/((2x+1)^2)) ?
The first derivative of (250000x^2/((2x+1)^2)) is (500000x)/((2x+1)^3)