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Popular >

derivative of ln((3+x/(3-x)))

Solution

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

Solution

\frac{6}{( x + 3 ) ( - x + 3 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 + x}{3 - x}) = \frac{6}{( 3 - x ) ^{2}}

= \frac{1}{\frac{3 + x}{3 - x}} \cdot \frac{6}{( 3 - x ) ^{2}}

Simplify

\frac{1}{\frac{3 + x}{3 - x}} \cdot \frac{6}{( 3 - x ) ^{2}} : \frac{6}{( x + 3 ) ( - x + 3 )}

= \frac{6}{( x + 3 ) ( - x + 3 )}

Popular Examples

integral from 0 to 1 of (3e^x-3xe^{x^2})

\int_{0}^{1} (3 e^{x} - 3 x e^{x^{2}}) d x

integral of 8cos(sqrt(x))

\int 8 cos (x) d x

limit as x approaches pi of (cos^2(x))/x

x \to π lim (\frac{cos ^{2} ( x )}{x})

(\partial)/(\partial x)(1/2 yx^2)

\frac{\partial}{\partial x} (\frac{1}{2} y x^{2})

(\partial)/(\partial x)((x^2+y^2)^{1/3})

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{1}{3}})

Frequently Asked Questions (FAQ)

What is the derivative of ln((3+x/(3-x))) ?
The derivative of ln((3+x/(3-x))) is 6/((x+3)(-x+3))
What is the first derivative of ln((3+x/(3-x))) ?
The first derivative of ln((3+x/(3-x))) is 6/((x+3)(-x+3))