What is the derivative of b/((1-(y/x))) ?

The derivative of b/((1-(y/x))) is (bx)/((x-y)^2)

What is the first derivative of b/((1-(y/x))) ?

The first derivative of b/((1-(y/x))) is (bx)/((x-y)^2)

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derivative of

\frac{b}{( 1 - ( \frac{y}{x} ) )}

\frac{b x}{( x - y ) ^{2}}

Solution steps

\frac{d}{d y} (\frac{b}{1 - \frac{y}{x}})

Treat

b, x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= b \frac{d}{d y} (\frac{1}{1 - \frac{y}{x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= b \frac{d}{d y} ((1 - \frac{y}{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - \frac{y}{x} ) ^{2}} \frac{d}{d y} (1 - \frac{y}{x})

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

\frac{d}{d y} (1 - \frac{y}{x}) = - \frac{1}{x}

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

Simplify

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

= \frac{b x}{( x - y ) ^{2}}

What is the derivative of b/((1-(y/x))) ?
The derivative of b/((1-(y/x))) is (bx)/((x-y)^2)
What is the first derivative of b/((1-(y/x))) ?
The first derivative of b/((1-(y/x))) is (bx)/((x-y)^2)