What is the derivative of (50x/(sqrt(1000+3x))) ?

The derivative of (50x/(sqrt(1000+3x))) is (25(3x+2000))/((3x+1000)sqrt(3x+1000))

What is the first derivative of (50x/(sqrt(1000+3x))) ?

The first derivative of (50x/(sqrt(1000+3x))) is (25(3x+2000))/((3x+1000)sqrt(3x+1000))

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\frac{d}{d x} (\frac{50 x}{1000 + 3 x})

\frac{25 ( 3 x + 2000 )}{( 3 x + 1000 ) 3 x + 1000}

Solution steps

\frac{d}{d x} (\frac{50 x}{1000 + 3 x})

Take the constant out:

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

= 50 \frac{d}{d x} (\frac{x}{1000 + 3 x})

Apply the Quotient Rule:

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

= 50 \cdot \frac{\frac{d x}{d x} 1000 + 3 x - \frac{d}{d x} ( 1000 + 3 x ) x}{( 1000 + 3 x ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (1000 + 3 x) = \frac{3}{2 1000 + 3 x}

= 50 \cdot \frac{1 \cdot 1000 + 3 x - \frac{3}{2 1000 + 3 x} x}{( 1000 + 3 x ) ^{2}}

Simplify

50 \cdot \frac{1 \cdot 1000 + 3 x - \frac{3}{2 1000 + 3 x} x}{( 1000 + 3 x ) ^{2}} : \frac{25 ( 3 x + 2000 )}{( 3 x + 1000 ) 3 x + 1000}

= \frac{25 ( 3 x + 2000 )}{( 3 x + 1000 ) 3 x + 1000}

\int e^{8 x + 1} d x

y = 1 + 3 x, x = 0, x = 8, y = 0

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

\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

y^{^{'}} = \frac{x}{y ^{2}}

What is the derivative of (50x/(sqrt(1000+3x))) ?
The derivative of (50x/(sqrt(1000+3x))) is (25(3x+2000))/((3x+1000)sqrt(3x+1000))
What is the first derivative of (50x/(sqrt(1000+3x))) ?
The first derivative of (50x/(sqrt(1000+3x))) is (25(3x+2000))/((3x+1000)sqrt(3x+1000))