What is the derivative of 1500x+3000(2x+3^{-1}-1000) ?

The derivative of 1500x+3000(2x+3^{-1}-1000) is -(6000)/((2x+3)^2)+1500

What is the first derivative of 1500x+3000(2x+3^{-1}-1000) ?

The first derivative of 1500x+3000(2x+3^{-1}-1000) is -(6000)/((2x+3)^2)+1500

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\frac{d}{d x} (1500 x + 3000 (2 x + 3)^{- 1} - 1000)

- \frac{6000}{( 2 x + 3 ) ^{2}} + 1500

Solution steps

\frac{d}{d x} (1500 x + 3000 (2 x + 3)^{- 1} - 1000)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1500 x) + \frac{d}{d x} (3000 (2 x + 3)^{- 1}) - \frac{d}{d x} (1000)

\frac{d}{d x} (1500 x) = 1500

\frac{d}{d x} (3000 (2 x + 3)^{- 1}) = - \frac{6000}{( 2 x + 3 ) ^{2}}

\frac{d}{d x} (1000) = 0

= 1500 - \frac{6000}{( 2 x + 3 ) ^{2}} - 0

Simplify

= - \frac{6000}{( 2 x + 3 ) ^{2}} + 1500

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What is the derivative of 1500x+3000(2x+3^{-1}-1000) ?
The derivative of 1500x+3000(2x+3^{-1}-1000) is -(6000)/((2x+3)^2)+1500
What is the first derivative of 1500x+3000(2x+3^{-1}-1000) ?
The first derivative of 1500x+3000(2x+3^{-1}-1000) is -(6000)/((2x+3)^2)+1500