What is the derivative of f(b)= b/(z+n) ?

The derivative of f(b)= b/(z+n) is -b/((z+n)^2)

What is the first derivative of f(b)= b/(z+n) ?

The first derivative of f(b)= b/(z+n) is -b/((z+n)^2)

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derivative of

f (b) = \frac{b}{z + n}

- \frac{b}{( z + n ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{b}{z + n})

Take the constant out:

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

= b \frac{d}{d z} (\frac{1}{z + n})

Apply exponent rule:

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

= b \frac{d}{d z} ((z + n)^{- 1})

Apply the chain rule:

- \frac{1}{( z + n ) ^{2}} \frac{d}{d z} (z + n)

= - \frac{1}{( z + n ) ^{2}} \frac{d}{d z} (z + n)

\frac{d}{d z} (z + n) = 1

= b (- \frac{1}{( z + n ) ^{2}} \cdot 1)

Simplify

b (- \frac{1}{( z + n ) ^{2}} \cdot 1) : - \frac{b}{( z + n ) ^{2}}

= - \frac{b}{( z + n ) ^{2}}

\int \frac{( 6 x ^{2} + 5 x + 6 )}{( x ^{2} + 1 ) ^{2}} d x

\frac{d S}{d r} = k S

\int sin^{3} (u) d u

\frac{d}{d x} ((ln (x))^{- 1})

y = x^{\frac{4}{3}}

What is the derivative of f(b)= b/(z+n) ?
The derivative of f(b)= b/(z+n) is -b/((z+n)^2)
What is the first derivative of f(b)= b/(z+n) ?
The first derivative of f(b)= b/(z+n) is -b/((z+n)^2)