What is the derivative of (sqrt(x)/(7x+8)) ?

The derivative of (sqrt(x)/(7x+8)) is (-7x+8)/(2sqrt(x)(7x+8)^2)

What is the first derivative of (sqrt(x)/(7x+8)) ?

The first derivative of (sqrt(x)/(7x+8)) is (-7x+8)/(2sqrt(x)(7x+8)^2)

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\frac{d}{d x} (\frac{x}{7 x + 8})

\frac{- 7 x + 8}{2 x ( 7 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{7 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( 7 x + 8 ) - \frac{d}{d x} ( 7 x + 8 ) x}{( 7 x + 8 ) ^{2}}

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

\frac{d}{d x} (7 x + 8) = 7

= \frac{\frac{1}{2 x} ( 7 x + 8 ) - 7 x}{( 7 x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 7 x + 8 ) - 7 x}{( 7 x + 8 ) ^{2}} : \frac{- 7 x + 8}{2 x ( 7 x + 8 ) ^{2}}

= \frac{- 7 x + 8}{2 x ( 7 x + 8 ) ^{2}}

\frac{\partial}{\partial x} (2 x - \frac{3}{x ^{2}} + y)

y = 2 - x

y^{^{''}} - y^{^{'}} + 5 y = 3

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

y^{^{''}} + 4 y = x^{2} + 3 e^{x}

What is the derivative of (sqrt(x)/(7x+8)) ?
The derivative of (sqrt(x)/(7x+8)) is (-7x+8)/(2sqrt(x)(7x+8)^2)
What is the first derivative of (sqrt(x)/(7x+8)) ?
The first derivative of (sqrt(x)/(7x+8)) is (-7x+8)/(2sqrt(x)(7x+8)^2)