What is the derivative of (150000/((4x+75)^2)) ?

The derivative of (150000/((4x+75)^2)) is -(1200000)/((4x+75)^3)

What is the first derivative of (150000/((4x+75)^2)) ?

The first derivative of (150000/((4x+75)^2)) is -(1200000)/((4x+75)^3)

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\frac{d}{d x} (\frac{150000}{( 4 x + 75 ) ^{2}})

- \frac{1200000}{( 4 x + 75 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{150000}{( 4 x + 75 ) ^{2}})

Take the constant out:

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

= 150000 \frac{d}{d x} (\frac{1}{( 4 x + 75 ) ^{2}})

Apply exponent rule:

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

= 150000 \frac{d}{d x} ((4 x + 75)^{- 2})

Apply the chain rule:

- \frac{2}{( 4 x + 75 ) ^{3}} \frac{d}{d x} (4 x + 75)

= - \frac{2}{( 4 x + 75 ) ^{3}} \frac{d}{d x} (4 x + 75)

\frac{d}{d x} (4 x + 75) = 4

= 150000 (- \frac{2}{( 4 x + 75 ) ^{3}} \cdot 4)

Simplify

150000 (- \frac{2}{( 4 x + 75 ) ^{3}} \cdot 4) : - \frac{1200000}{( 4 x + 75 ) ^{3}}

= - \frac{1200000}{( 4 x + 75 ) ^{3}}

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4 sin^{2} (0.5 t) + 1

f (x) = 3 x, at x = 4

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What is the derivative of (150000/((4x+75)^2)) ?
The derivative of (150000/((4x+75)^2)) is -(1200000)/((4x+75)^3)
What is the first derivative of (150000/((4x+75)^2)) ?
The first derivative of (150000/((4x+75)^2)) is -(1200000)/((4x+75)^3)