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

The derivative of (xsqrt(2x+1)/(sqrt(4-5x))) is (-20x^2+19x+8)/(2(4-5x)sqrt(2x+1)\sqrt{-5x+4)}

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

The first derivative of (xsqrt(2x+1)/(sqrt(4-5x))) is (-20x^2+19x+8)/(2(4-5x)sqrt(2x+1)\sqrt{-5x+4)}

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

\frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (4 - 5 x) = - \frac{5}{2 4 - 5 x}

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

Simplify

\frac{\frac{3 x + 1}{2 x + 1} 4 - 5 x - ( - \frac{5}{2 4 - 5 x} ) x 2 x + 1}{( 4 - 5 x ) ^{2}} : \frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

= \frac{- 20 x ^{2} + 19 x + 8}{2 ( 4 - 5 x ) 2 x + 1 - 5 x + 4}

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

\int q^{2} cos (4 q) d q

3 x^{2} + 3 x - 5

\frac{\partial}{\partial x} (\frac{2 x}{y})

y = x^{4} e^{3 x}

What is the derivative of (xsqrt(2x+1)/(sqrt(4-5x))) ?
The derivative of (xsqrt(2x+1)/(sqrt(4-5x))) is (-20x^2+19x+8)/(2(4-5x)sqrt(2x+1)\sqrt{-5x+4)}
What is the first derivative of (xsqrt(2x+1)/(sqrt(4-5x))) ?
The first derivative of (xsqrt(2x+1)/(sqrt(4-5x))) is (-20x^2+19x+8)/(2(4-5x)sqrt(2x+1)\sqrt{-5x+4)}