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

The derivative of y=sqrt(x/(x+7)) is 7/(2sqrt(x)(x+7)^{3/2)}

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

The first derivative of y=sqrt(x/(x+7)) is 7/(2sqrt(x)(x+7)^{3/2)}

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derivative of

y = \frac{x}{x + 7}

\frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

\frac{1}{2 \frac{x}{x + 7}} \frac{d}{d x} (\frac{x}{x + 7})

= \frac{1}{2 \frac{x}{x + 7}} \frac{d}{d x} (\frac{x}{x + 7})

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

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

Simplify

\frac{1}{2 \frac{x}{x + 7}} \cdot \frac{7}{( x + 7 ) ^{2}} : \frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

= \frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

64 x - 0.02 x^{2}

f (x) = 3 x^{2} + x, at x = 1

sin^{2} (t)

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

\int_{1}^{1 - 2 y} \frac{y}{x} d x

What is the derivative of y=sqrt(x/(x+7)) ?
The derivative of y=sqrt(x/(x+7)) is 7/(2sqrt(x)(x+7)^{3/2)}
What is the first derivative of y=sqrt(x/(x+7)) ?
The first derivative of y=sqrt(x/(x+7)) is 7/(2sqrt(x)(x+7)^{3/2)}