What is the derivative of (2*k/(x+d)) ?

The derivative of (2*k/(x+d)) is -(2k)/((x+d)^2)

What is the first derivative of (2*k/(x+d)) ?

The first derivative of (2*k/(x+d)) is -(2k)/((x+d)^2)

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\frac{d}{d x} (\frac{2 \cdot k}{x + d})

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

Solution steps

\frac{d}{d x} (\frac{2 k}{x + d})

Treat

k, d

as a constant

Take the constant out:

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

= 2 k \frac{d}{d x} (\frac{1}{x + d})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of (2*k/(x+d)) ?
The derivative of (2*k/(x+d)) is -(2k)/((x+d)^2)
What is the first derivative of (2*k/(x+d)) ?
The first derivative of (2*k/(x+d)) is -(2k)/((x+d)^2)