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Popular >

derivative of y=sqrt(x/(x+3))

Solution

derivative of

y = \frac{x}{x + 3}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of cos(x/4)

\frac{d}{d x} (cos (\frac{x}{4}))

y^{''}-4y^'+4y=(3x+8)e^{2x}+8x^2

y^{^{''}} - 4 y^{^{'}} + 4 y = (3 x + 8) e^{2 x} + 8 x^{2}

integral of yln(y)-1/(sqrt(9-y^2))

\int y ln (y) - \frac{1}{9 - y ^{2}} d y

(\partial)/(\partial x)(2x-10)

\frac{\partial}{\partial x} (2 x - 10)

integral of ksqrt(t)

\int k t d t

Frequently Asked Questions (FAQ)

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