What is the derivative of (-5)/((4x-2y+2)) ?

The derivative of (-5)/((4x-2y+2)) is 5/((2x+1-y)^2)

What is the first derivative of (-5)/((4x-2y+2)) ?

The first derivative of (-5)/((4x-2y+2)) is 5/((2x+1-y)^2)

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derivative of

\frac{- 5}{( 4 x - 2 y + 2 )}

\frac{5}{( 2 x + 1 - y ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 5}{4 x - 2 y + 2})

Simplify

\frac{- 5}{4 x - 2 y + 2} : - \frac{5}{4 x - 2 y + 2}

= \frac{d}{d x} (- \frac{5}{4 x - 2 y + 2})

Treat

y

as a constant

Take the constant out:

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

= - 5 \frac{d}{d x} (\frac{1}{4 x - 2 y + 2})

Apply exponent rule:

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

= - 5 \frac{d}{d x} ((4 x - 2 y + 2)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 x - 2 y + 2 ) ^{2}} \frac{d}{d x} (4 x - 2 y + 2)

= - \frac{1}{( 4 x - 2 y + 2 ) ^{2}} \frac{d}{d x} (4 x - 2 y + 2)

\frac{d}{d x} (4 x - 2 y + 2) = 4

= - 5 (- \frac{1}{( 4 x - 2 y + 2 ) ^{2}} \cdot 4)

Simplify

- 5 (- \frac{1}{( 4 x - 2 y + 2 ) ^{2}} \cdot 4) : \frac{5}{( 2 x + 1 - y ) ^{2}}

= \frac{5}{( 2 x + 1 - y ) ^{2}}

y = 5 x^{8} - 6 x + 12

f (t) = 3 + 8 t - t^{2}

x^{2} cos (\frac{1}{x})

y = x^{2} + 5

20 q - 2 q^{2}

What is the derivative of (-5)/((4x-2y+2)) ?
The derivative of (-5)/((4x-2y+2)) is 5/((2x+1-y)^2)
What is the first derivative of (-5)/((4x-2y+2)) ?
The first derivative of (-5)/((4x-2y+2)) is 5/((2x+1-y)^2)