What is the derivative of a/(1-bx) ?

The derivative of a/(1-bx) is (ab)/((1-bx)^2)

What is the first derivative of a/(1-bx) ?

The first derivative of a/(1-bx) is (ab)/((1-bx)^2)

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derivative of

\frac{a}{1 - b x}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} - 5 y = x^{2}

\frac{7}{x}, - 1

y^{^{'}} + 4 y = 1, y (0) = 1

f (x) = x^{2} + 16, at x = - 3

(x + 5) cos (x)

What is the derivative of a/(1-bx) ?
The derivative of a/(1-bx) is (ab)/((1-bx)^2)
What is the first derivative of a/(1-bx) ?
The first derivative of a/(1-bx) is (ab)/((1-bx)^2)