What is the derivative of 60d(12+x^{-1}) ?

The derivative of 60d(12+x^{-1}) is -(60d)/((12+x)^2)

What is the first derivative of 60d(12+x^{-1}) ?

The first derivative of 60d(12+x^{-1}) is -(60d)/((12+x)^2)

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\frac{d}{d x} (60 d (12 + x)^{- 1})

- \frac{60 d}{( 12 + x ) ^{2}}

Solution steps

\frac{d}{d x} (60 d (12 + x)^{- 1})

Treat

d

as a constant

Take the constant out:

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

= 60 d \frac{d}{d x} ((12 + x)^{- 1})

Apply the chain rule:

- \frac{1}{( 12 + x ) ^{2}} \frac{d}{d x} (12 + x)

= - \frac{1}{( 12 + x ) ^{2}} \frac{d}{d x} (12 + x)

\frac{d}{d x} (12 + x) = 1

= 60 d (- \frac{1}{( 12 + x ) ^{2}} \cdot 1)

Simplify

60 d (- \frac{1}{( 12 + x ) ^{2}} \cdot 1) : - \frac{60 d}{( 12 + x ) ^{2}}

= - \frac{60 d}{( 12 + x ) ^{2}}

\frac{\partial}{\partial y} (x^{4} e^{x y})

\int_{1}^{\infty} \frac{1}{( 2 k + 23 )} d k

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What is the derivative of 60d(12+x^{-1}) ?
The derivative of 60d(12+x^{-1}) is -(60d)/((12+x)^2)
What is the first derivative of 60d(12+x^{-1}) ?
The first derivative of 60d(12+x^{-1}) is -(60d)/((12+x)^2)