What is the derivative of (2ab/((a-bx)^2)) ?

The derivative of (2ab/((a-bx)^2)) is (4ab^2)/((a-bx)^3)

What is the first derivative of (2ab/((a-bx)^2)) ?

The first derivative of (2ab/((a-bx)^2)) is (4ab^2)/((a-bx)^3)

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\frac{d}{d x} (\frac{2 ab}{( a - b x ) ^{2}})

\frac{4 a b ^{2}}{( a - b x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 ab}{( a - b x ) ^{2}})

Take the constant out:

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

= 2 ab \frac{d}{d x} (\frac{1}{( a - b x ) ^{2}})

Apply exponent rule:

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

= 2 ab \frac{d}{d x} ((a - b x)^{- 2})

Apply the chain rule:

- \frac{2}{( a - b x ) ^{3}} \frac{d}{d x} (a - b x)

= - \frac{2}{( a - b x ) ^{3}} \frac{d}{d x} (a - b x)

\frac{d}{d x} (a - b x) = - b

= 2 ab (- \frac{2}{( a - b x ) ^{3}} (- b))

Simplify

2 ab (- \frac{2}{( a - b x ) ^{3}} (- b)) : \frac{4 a b ^{2}}{( a - b x ) ^{3}}

= \frac{4 a b ^{2}}{( a - b x ) ^{3}}

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x \to 0 lim (\frac{2}{sin ( 7 x )})

What is the derivative of (2ab/((a-bx)^2)) ?
The derivative of (2ab/((a-bx)^2)) is (4ab^2)/((a-bx)^3)
What is the first derivative of (2ab/((a-bx)^2)) ?
The first derivative of (2ab/((a-bx)^2)) is (4ab^2)/((a-bx)^3)