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Popular >

derivative of y=ln(2+x)+2/(2+x)

Solution

derivative of

y = ln (2 + x) + \frac{2}{2 + x}

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (2 + x)) + \frac{d}{d x} (\frac{2}{2 + x})

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

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

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

Simplify

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

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

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(\partial)/(\partial x)(sin(x)+pi*cos(y))

\frac{\partial}{\partial x} (sin (x) + π \cdot cos (y))

x(dy)/(dx)+2y=sin(x)

x \frac{d y}{d x} + 2 y = sin (x)

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\int \frac{e ^{8 x}}{x} d x

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x \to 0 lim (csc^{2} (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(2+x)+2/(2+x) ?
The derivative of y=ln(2+x)+2/(2+x) is x/((x+2)^2)
What is the first derivative of y=ln(2+x)+2/(2+x) ?
The first derivative of y=ln(2+x)+2/(2+x) is x/((x+2)^2)