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Popular >

derivative of y=ln((5x)/(7+x))

Solution

derivative of

y = ln (\frac{5 x}{7 + x})

Solution

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

Solution steps

\frac{d}{d x} (ln (\frac{5 x}{7 + x}))

Apply the chain rule:

\frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

= \frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

\frac{d}{d x} (\frac{5 x}{7 + x}) = \frac{35}{( 7 + x ) ^{2}}

= \frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}}

Simplify

\frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}} : \frac{7}{x ( x + 7 )}

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

Popular Examples

derivative of (x+1/x)^2 derivative of

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

(\partial)/(\partial x)(1/((x^2+y^2)))

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

(x^4+y^4)dx-(xy^3)dy=0

(x^{4} + y^{4}) d x - (x y^{3}) d y = 0

integral of 1/((x^2+25)^2)

\int \frac{1}{( x ^{2} + 25 ) ^{2}} d x

derivative of f(x)=(9/8)x^{8/9}derivative of

f (x) = (\frac{9}{8}) x^{\frac{8}{9}}

Frequently Asked Questions (FAQ)

What is the derivative of y=ln((5x)/(7+x)) ?
The derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))
What is the first derivative of y=ln((5x)/(7+x)) ?
The first derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))