What is the derivative of 1000(18^3-x^{1/3}) ?

The derivative of 1000(18^3-x^{1/3}) is -(1000)/(3(5832-x)^{2/3)}

What is the first derivative of 1000(18^3-x^{1/3}) ?

The first derivative of 1000(18^3-x^{1/3}) is -(1000)/(3(5832-x)^{2/3)}

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\frac{d}{d x} (1000 (1 8^{3} - x)^{\frac{1}{3}})

- \frac{1000}{3 ( 5832 - x ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (1000 (1 8^{3} - x)^{\frac{1}{3}})

Simplify

1000 (1 8^{3} - x)^{\frac{1}{3}} : 1000 (5832 - x)^{\frac{1}{3}}

= \frac{d}{d x} (1000 (5832 - x)^{\frac{1}{3}})

Take the constant out:

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

= 1000 \frac{d}{d x} ((5832 - x)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 5832 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (5832 - x)

= \frac{1}{3 ( 5832 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (5832 - x)

\frac{d}{d x} (5832 - x) = - 1

= 1000 \cdot \frac{1}{3 ( 5832 - x ) ^{\frac{2}{3}}} (- 1)

Simplify

1000 \cdot \frac{1}{3 ( 5832 - x ) ^{\frac{2}{3}}} (- 1) : - \frac{1000}{3 ( 5832 - x ) ^{\frac{2}{3}}}

= - \frac{1000}{3 ( 5832 - x ) ^{\frac{2}{3}}}

x \to 6 + lim (x^{2} - 36)

8 (e^{x} cos (x) - e^{x} sin (x))

x \to - 1 lim (\frac{1}{x ^{3} - x})

y^{8} - \frac{y ^{9} + 4}{x ^{3} 4 y ^{^{'}}} = 0

\int (- x x^{4}) d x

What is the derivative of 1000(18^3-x^{1/3}) ?
The derivative of 1000(18^3-x^{1/3}) is -(1000)/(3(5832-x)^{2/3)}
What is the first derivative of 1000(18^3-x^{1/3}) ?
The first derivative of 1000(18^3-x^{1/3}) is -(1000)/(3(5832-x)^{2/3)}